GIFT  OF 
Irs.    Sara;,  P.  '.Valsworth 


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to  if  XT  is 


PATH   OF   BIELA 


LETTERS 

ON 

ASTRONOMY, 

ADDRESSED  TO  A  LADY: 

IN  WHICH 

THE  ELEMENTS  OF  THE  SCIENCE 

ABE 

FAMILIARLY    EXPLAINED    IN    CONNEXION    WITH 

""    ITS 

• 

LITERARY    HISTORY. 

WITH  NUMEROUS  ENGRAVINGS. 


BY  DENISON   OLMSTED,  A.  M. 

PROFESSOR  OF  NATURAL  PHILOSOPHY  AND  ASTRONOMY  IN  YALE  COLLEGE  j   MEM- 
BER OF  THE  CONNECTICUT  BOARD  OF  COMMISSIONERS  FOR  COMMON 

SCHOOLS;  AUTHOR  OF  INTRODUCTION  TO  NATURAL 
PHILOSOPHY,  AND  ASTRONOMY,  ETC.  ETC. 


BOSTON: 

MARSH,  CAPEN,  LYON,  AND  WEBB, 
1841. 


Entered  according  to  Act  of  Congress,  in  the  year  1840,  by 

MARSH,  CAPEN,  LYON,  AND  WEBB, 
in  the  Clerk's  Office  of  the  District  Court  of  Massachusetts. 


EDUCATION   PRESS. 


"  IF  the  present  age  is  distinguished  by  more  clear 
and  just  views  of  social  and  political  science,  it  is  not 
less  marked  by  the  disposition,  so  unequivocally  and 
universally  manifested,  to  reject  the  inordinate  estimate 
heretofore  set  upon  merely  ornamental  literature ;  and 
whilst  it  does  not  refuse  their  just  rank  and  influence 
to  such  studies,  it  admits  to  that  high  consideration  to 
which  they  are  entitled,  the  sciences  which  explain  the 
beautiful  phenomena  of  the  physical  world. 

"  The  public  now  demand  of  those  professionally 
devoted  to  the  sciences,  that  they  shall  not  confine  the 
knowledge  they  have  such  favored  opportunities  of  ac- 
quiring, to  the  lecture-room,  but  shall  render  it,  as  far  as 
practicable,  available  to  the  well-informed  of  all  profes- 
sions, and  to  the  more  intelligent,  at  least,  of  the  other 
sex." — Edinburgh  Review  for  April,  1835. 


CONTENTS 


PREFACE,      ...*...    ^ 3 

LETTER  I. 
Introductory  Observations,      >".  "\     . 9 

LETTER  II. 
Doctrine  of  the  Sphere, 16 

LETTER  III. 
Astronomical  Instruments. — Telescope, 29 

LETTER  IV. 
Telescope  continued,        36 

LETTER  V. 
Observatories, 45t 

LETTER  VI. 
Time  and  the  Calendar,  .     •.'.'. 59 

LETTER  VII. 

Figure  of  the  Earth,    .     .     .     .     .     ;-T^.    f-'\     .     69 

LETTER  VIII. 

Diurnal  Revolution,     .  •/'".'•*."   '.;•  ;  .v^v    ...     81 

LETTER  IX. 

Parallax  and  Refrartion,       «»«!«  v* 89 

1* 


6  CONTENTS. 

LETTER  X. 
The  Sun, 101 

LETTER  XI. 
Annual  Revolution. — Seasons,        Ill 

LETTER  XII. 
Laws  of  Motion, 126 

LETTER  XIII. 
Terrestrial  Gravity, 134 

LETTER  XIV. 

Sir  Isaac  Newton. — Universal  Gravitation. — Figure 
of  the  Earth's  Orbit. — Precession  of  the  Equinoxes,    \  43 

LETTER  XV. 
The  Moon, 157 

LETTER  XVI. 

The  Moon. — Phases. — Harvest  Moon. — Librations,  .   172 

LETTER  XVII. 
Moon's  Orbit. — Her  Irregularities, 180 

LETTER  XVIII. 
Eclipses, 195 

LETTER  XIX. 

Longitude. — Tides, 208 

LETTER  XX. 

Planets. — Mercury  and  Venus, 225 

LETTER  XXI. 
Superior  Planets  :  Mars,  Jupiter,  Saturn,  and  Uranus,  243 


CONTENTS.  7 

LETTER  XXII. 
Copernicus. — Galileo,      .     .     .     ....     .     .     .  254 

LETTER  XXIII. 
Saturn. — Uranus. — Asteroids,  .     .     ....     .     .  274 

LETTER  XXIV. 
The  Planetary  Motions. — Kepler's  Laws. — Kepler,  .  291 

LETTER  XXV. 
Comets, 312 

LETTER  XXVI. 
Comets, .     .334 

LETTER  XXVII. 
Meteoric  Showers, .  346 

LETTER  XXVIII. 

Fixed  Stars, ."V.     .     .  365 

LETTER  XXIX. 

Fixed  Stars,  .     .     .    .     .     .     .     / 383 

LETTER  XXX. 

System  of  the  World,       .     .     .     .     .; 392 

LETTER  XXXI. 
Conclusion,   .     ....    V 406 

INDEX, ..';  .     .  415 


LETTERS  ON  ASTRONOMY. 


LETTER  I. 

INTRODUCTORY  OBSERVATIONS. 

"Ye  sacred  Muses,  -with  whose  beauty  fired, 
My  soul  is  ravished,  and  my  brain  inspired, 
Whose  priest  I  am,  whose  holy  fillets  wear  ; 
Would  you  your  poet's  first  petition  hear, 
Give  me  the  ways  of  wandering  stars  to  know, 
The  depths  of  heaven  above,  and  earth  below ; 
Teach  me  the  various  labors  of  the  moon, 
And  whence  proceed  th'  eclipses  of  the  sun; 
Why  flowing  tides  prevail  upon  the  main, 
And  in  what  dark  recess  they  shrink  again  ; 
What  shakes  the  solid  earth,  what  cause  delays 
The  Summer  nights,  and  shortens  Winter  days." 

Dryden's  Virgil. 

To  MRS.  C M . 

DEAR  MADAM, — In  the  conversation  we  recently  held 
on  the  study  of  Astronomy,  you  expressed  a  strong 
desire  to  become  better  acquainted  with  this  noble  sci- 
ence, but  said  you  had  always  been  repelled  by  the  air 
of  severity  which  it  exhibits,  arrayed  as  it  is  in  so  many 
technical  terms,  and  such  abstruse  mathematical  pro- 
cesses :  or,  if  you  had  taken  up  some  smaller  treatise, 
with  the  hope  of  avoiding  these  perplexities,  you  had 
always  found  it  so  meager  and  superficial,  as  to  afford 
you  very  little  satisfaction.  You  asked,  if  a  work  might 
not  be  prepared,  which  would  convey  to  the  general 
reader  some  clear  and  adequate  knowledge  of  the  great 
discoveries  in  astronomy,  and  yet  require  for  its  perusal 
no  greater  preparation,  than  may  be  presumed  of  every 
well-educated  English  scholar  of  either  sex. 

You  were  pleased  to  add  the  request,  that  I  would 


10  LETTERS  ON  ASTRONOMY. 

write  such  a  work, — a  work  which  should  combine, 
with  a  luminous  exposition  of  the  leading  truths  of  the 
science,  some  account  of  the  interesting  historical  facts 
with  which  it  is  said  the  records  of  astronomical  dis- 
covery abound.  Having,  moreover,  heard  much  of  the 
grand  discoveries  which,  within  the  last  fifty  years,  have 
been  made  among  the  fixed  stars,  you  expressed  a 
strong  desire  to  learn  more  respecting  these  sublime 
researches.  Finally,  you  desired  to  see  the  argument 
for  the  existence  and  natural  attributes  of  the  Deity,  as 
furnished  by  astronomy,  more  fully  and  clearly  exhibit- 
ed, than  is  done  in  any  work  which  you  have  hitherto 
perused.  In  the  preparation  of  the  proposed  treatise, 
you  urged  me  to  supply,  either  in  the  text  or  in  notes, 
every  elementary  principle  which  would  be  essential 
to  a  perfect  understanding  of  the  work  ;  for  although, 
while  at  school,  you  had  paid  some  attention  to  geom- 
etry and  natural  philosophy,  yet  so  much  time  had 
since  elapsed,  that  your  memory  required  to  be  re- 
freshed on  the  most  simple  principles  of  these  elemen- 
tary studies,  and  you  preferred  that  I  should  consider 
you  as  altogether  unacquainted  with  them. 

Although,  to  satisfy  a  mind,  so  cultivated  and  inquisi- 
tive as  yours,  may  require  a  greater  variety  of  powers 
and  attainments  than  I  possess,  yet,  as  you  were  pleased 
to  urge  me  to  the  trial,  I  have  resolved  to  make  the  at- 
tempt, and  will  see  how  far  I  may  be  able  to  lead  you 
into  the  interior  of  this  beautiful  temple,  without  oblig- 
ing you  to  force  your  way  through  the  "jargon  of  the 
schools." 

Astronomy,  however,  is  a  very  difficult  or  a  compar- 
atively easy  study,  according  to  the  view  we  take  of  it. 
The  investigation  of  the  great  laws  which  govern  the 
motions  of  the  heavenly  bodies  has  commanded  the 
highest  efforts  of  the  human  mind  ;  but  profound  truths, 
which  it  required  the  mightiest  efforts  of  the  intellect  to 
disclose,  are  often,  when  once  discovered,  simple  in  their 
complexion,  and  may  be  expressed  in  very  simple  terms. 
Thus,  the  creation  of  that  element,  on  whose  mysteri- 


INTRODUCTORY  OBSERVATIONS.  11 

ous  agency  depend  all  the  forms  of  beauty  and  loveli- 
ness, is  enunciated  in  these  few  monosyllables,  "And 
God  said,  let  there  be  light,  and  there  was  light ;"  and 
the  doctrine  of  universal  gravitation,  which  is  the  key 
that  unlocks  the  mysteries  of  the  universe,  is  simply 
this, — that  every  portion  of  matter  in  the  universe  tends 
towards  every  other.  The  three  great  laws  of  motion, 
also,  are,  when  stated,  so  plain,  that  they  seem  hardly 
to  assert  any  thing  but  what  we  knew  before.  That 
all  bodies,  if  at  rest,  will  continue  so,  as  is  declared  by 
the  first  law  of  motion.,  until  some  force  moves  them  ; 
or,  if  in  motion,  will  continue  so,  until  some  force  stops 
them,  appears  so  much  a  matter  of  course,  that  we  can 
at  first  hardly  see  any  good  reason  why  it  should  be 
dignified  with  the  title  of  the  first  great  law  of  motion  ; 
and  yet  it  contains  a  truth  which  it  required  profound 
sagacity  to  discover  and  expound. 

It  is,  therefore,  a  pleasing  consideration  to  those  who 
have  not  either  the  leisure  or  the  ability  to  follow  the 
astronomer  through  the  intricate  and  laborious  processes, 
which  conducted  him  to  his  great  discoveries,  that  they 
may  fully  avail  themselves  of  the  results  of  this  vast  toil, 
and  easily  understand  truths  which  it  required  ages  of 
the  severest  labor  to  unfold.  The  descriptive  parts  of 
astronomy,  or  what  may  be  called  the  natural  history 
of  the  heavens,  is  still  more  easily  understood  than  the 
laws  of  the  celestial  motions.  The  revelations  of  the 
telescope,  and  the  wonders  it  has  disclosed  in  the 
sun,  in  the  moon,  in  the  planets,  and  especially  in  the 
fixed  stars,  are  facts  not  difficult  to  be  understood,  al- 
though they  may  affect  the  mind  with  astonishment. 

The  great  practical  purpose  of  astronomy  to  the 
world  is,  enabling  us  safely  to  navigate  the  ocean. 
There  are  indeed  many  other  benefits  which  it  confers 
on  man  ;  but  this  is  the  most  important.  If,  however, 
you  ask,  what  advantages  the  study  of  astronomy 
promises,  as  a  branch  of  education,  I  answer,  that 
few  subjects  promise  to  the  mind  so  much  profit  and 
entertainment.  It  is  agreed  by  writers  on  the  human 


12  LETTERS  ON  ASTRONOMY. 

mind,  that  the  intellectual  powers  are  enlarged  and 
strengthened  by  the  habitual  contemplation  of  great 
objects,  while  they  are  contracted  and  weakened  by 
being  constantly  employed  upon  little  or  trifling  sub- 
jects. The  former  elevate,  the  latter  depress,  the 
mind,  to  their  own  level.  Now,  every  thing  in  as- 
tronomy is  great.  The  magnitudes,  distances,  and 
motions,  of  the  heavenly  bodies  ;  the  amplitude  of  the 
firmament  itself ;  and  the  magnificence  of  the  orbs  with 
which  it  is  lighted,  supply  exhaustless  materials  for 
contemplation,  and  stimulate  the  mind  to  its  noblest 
efforts.  The  emotion  felt  by  the  astronomer  is  not  that 
sudden  excitement  or  ecstasy,  which  wears  out  life,  but 
it  is  a  continued  glow  of  exalted  feeling,  which  gives 
the  sensation  of  breathing  in  a  purer  atmosphere  than 
others  enjoy.  We  should  at  first  imagine,  that  a  study 
which  calls  upon  its  votaries  for  the  severest  efforts  of 
the  human  intellect,  which  demands  the  undivided  toil 
of  years,  and  which  robs  the  night  of  its  accustomed 
hours  of  repose,  would  abridge  the  period  of  life ;  but 
it  is  a  singular  fact,  that  distinguished  astronomers,  as  a 
class,  have  been  remarkable  for  longevity.  I  know  not 
how  to  account  for  this  fact,  unless  we  suppose  that 
the  study  of  astronomy  itself  has  something  inherent  in 
it,  which  sustains  its  votaries  by  a  peculiar  aliment. 

It  is  the  privilege  of  the  student  of  this  department 
of  Nature,  that  his  cabinet  is  already  collected,  and  is 
ever  before  him  ;  and  he  is  exempted  from  the  toil  of 
collecting  his  materials  of  study  and  illustration,  by 
traversing  land  and  sea,  or  by  penetrating  into  the 
depths  of  the  earth.  Nor  are  they  in  their  nature  frail 
and  perishable.  No  sooner  is  the  veil  of  clouds  remov- 
ed, that  occasionally  conceals  the  firmament  by  night, 
than  his  specimens  are  displayed  to  view,  bright  and 
changeless.  The  renewed  pleasure  which  he  feels,  at 
every  new  survey  of  the  constellations,  grows  into  an  af- 
fection for  objects  which  have  so  often  ministered  to  his 
happiness.  His  imagination  aids  him  in  giving  them  a 
personification,  like  that  which  the  ancients  gave  to  the 


INTRODUCTORY  OBSERVATIONS.  13 

constellations  ;  (as  is  evident  from  the  names  which  they 
have  transmitted  to  us ;)  and  he  walks  abroad,  beneath 
the  evening  canopy,  with  the  conscious  satisfaction  and 
delight  of  being  in  the  presence  of  old  friends.  This 
emotion  becomes  stronger  when  he  wanders  far  from 
home.  Other  objects  of  his  attachment  desert  him ; 
the  face  of  society  changes ;  the  earth  presents  new 
features ;  but  the  same  sun  illumines  the  day,  the  same 
moon  adorns  the  night,  and  the  same  bright  stars  still 
attend  him. 

When,  moreover,  the  student  of  the  heavens  can 
command  the  aid  of  telescopes,  of  higher  and  higher 
powers,  new  acquaintances  are  made  every  evening. 
The  sight  of  each  new  member  of  the  starry  train,  that 
the  telescope  successively  reveals  to  him,  inspires  a  pe- 
culiar emotion  of  pleasure  ;  and  he  at  length  finds  him- 
self, whenever  he  sweeps  his  telescope  over  the  firma- 
ment, greeted  by  smiles,  unperceived  and  unknown  to 
his  fellow-mortals.  The  same  personification  is  given 
to  these  objects  as  to  the  constellations,  and  he  seems 
to  himself,  at  times,  when  he  has  penetrated  into  the 
remotest  depths  of  ether,  to  enjoy  the  high  prerogative 
of  holding  converse  with  the  celestials. 

It  is  no  small  encouragement,  to  one  who  wishes  to 
acquire  a  knowledge  of  the  heavens,  that  the  subject  is 
embarrassed  with  far  less  that  is  technical  than  most 
other  branches  of  natural  history.  Having  first  learned 
a  few  definitions,  and  the  principal  circles  into  which, 
for  convenience,  the  sphere  is  divided,  and  receiving 
the  great  laws  of  astronomy  on  the  authority  of  the 
eminent  persons  who  have  investigated  them,  you  will 
find  few  hard  terms,  or  technical  distinctions,  to  repel 
or  perplex  you  ;  and  you  will,  I  hope,  find  that  nothing 
but  an  intelligent  mind  and  fixed  attention  are  requi- 
site for  perusing  the  Letters  which  I  propose  to  address 
to  you.  I  shall  indeed  be  greatly  disappointed,  if  the 
perusal  does  not  inspire  you  with  some  portion  of  that 
pleasure,  which  I  have  described  as  enjoyed  by  the  as- 
tronomer himself. 

2  L.  A. 


14  LETTERS   ON  ASTRONOMY. 

The  dignity  of  the  study  of  the  heavenly  bodies,  and 
its  suitableness  to  the  most  refined  and  cultivated  mind, 
has  been  recognised  in  all  ages.  Virgil  celebrates  it  in 
the  beautiful  strains  with  which  I  have  headed  this  Let- 
ter, and  similar  sentiments  have  ever  been  cherished  by 
the  greatest  minds. 

As,  in  the  course  of  these  Letters,  I  propose  to  trace 
an  outline  of  the  history  of  astronomy,  from  the  earliest 
ages  to  the  present  time,  you  may  think  this  the  most 
suitable  place  for  introducing  it ;  but  the  successive 
discoveries  in  the  science  cannot  be  fully  understood 
and  appreciated,  until  after  an  acquaintance  has  been 
formed  with  the  science  itself.  We  must  therefore 
reserve  the  details  of  this  subject  for  a  future  opportu- 
nity ;  but  it  may  be  stated,  here,  that  astronomy  was 
cultivated  the  earliest  of  all  the  sciences ;  that  great 
attention  was  paid  to  it  by  several  very  ancient  nations, 
as  the  Egyptians  and  Chaldeans,  and  the  people  of  In- 
dia and  China,  before  it  took  its  rise  in  Greece.  More 
than  six  hundred  years  before  the  Christian  era,  howev- 
er, it  began  to  be  studied  in  this  latter  country.  Thales 
and  Pythagoras  were  particularly  distinguished  for  their 
devotion  to  this  science ;  and  the  celebrated  school  of 
Alexandria,  in  Egypt,  which  took  its  rise  about  three 
hundred  years  before  the  Christian  era,  and  flourished 
for  several  hundred  years,  numbered  among  its  disciples 
a  succession  of  eminent  astronomers,  among  whom  were 
Hipparchus,  Eratosthenes,  and  Ptolemy.  The  last  of 
these  composed  a  great  work  on  astronomy,  called  the 
c  Almagest,'  in  which  is  transmitted  to  us  an  account  of 
all  that  was  known  of  the  science  by  the  Alexandrian 
school.  The  '  Almagest'  was  the  principal  text-book 
in  astronomy,  for  many  centuries  afterwards,  and  com- 
paratively few  improvements  were  made  until  the  age 
of  Copernicus.  Copernicus  was  born  at  Thorn,  in 
Prussia,  in  1473.  Previous  to  his  time,  the  doctrine 
was  held,  that  the  earth  is  at  rest  in  the  centre  of  the 
universe,  and  that  the  sun,  moon,  and  stars,  revolve 
about  it,  every  day,  from  east  to  west ;  in  short,  that 


INTRODUCTORY  OBSERVATIONS.  15 

the  apparent  motions  of  the  heavenly  bodies  are  the 
same  with  their  real  motions.  But  Copernicus  ex- 
pounded what  is  now  known  to  be  the  true  theory  of 
the  celestial  motions,  in  which  the  sun  is  placed  in  the 
centre  of  the  solar  system,  and  the  earth  and  all  the 
planets  are  made  to  revolve  around  him,  from  west  to 
east,  while  the  apparent  diurnal  motion  of  the  heavenly 
bodies,  from  east  to  west,  is  explained  by  the  revolution 
of  the  earth  on  its  axis,  in  the  same  time,  from  west  to 
east ;  a  motion  of  which  we  are  unconscious,  and  which 
we  erroneously  ascribe  to  external  objects,  as  we  imag- 
ine the  shore  is  receding  from  us,  when  we  are  uncon- 
scious of  the  motion  of  the  ship  that  carries  us  from  it. 

Although  many  of  the  appearances,  presented  by  the 
motions  of  the  heavenly  bodies,  may  be  explained  on 
the  former  erroneous  hypothesis,  yet,  like  other  hypoth- 
eses founded  in  error,  it  was  continually  leading  its 
votaries  into  difficulties,  and  blinding  their  minds  to 
the  perception  of  truth.  They  had  advanced  nearly  as 
far  as  it  was  practicable  to  go  in  the  wrong  road ;  and 
the  great  and  sublime  discoveries  of  modern  times  are 
owing,  in  no  small  degree,  to  the  fact,  that,  since  the 
days  of  Copernicus,  astronomers  have  been  pursuing 
the  plain  and  simple  path  of  truth,  instead  of  threading 
their  way  through  the  mazes  of  error. 

Near  the  close,  of  the  sixteenth  century,  Tycho 
Brahe,  a  native  of  Sweden,  but  a  resident  of  Denmark, 
carried  astronomical  observations  (which  constitute  the 
basis  of  all  that  is  valuable  in  astronomy)  to  a  far 
greater  degree  of  perfection  than  had  ever  been  done 
before.  Kepler,  a  native  of  Germany,  one  of  the  great- 
est geniuses  the  world  has  ever  seen,  was  contemporary 
with  Tycho  Brahe,  and  was  associated  with  him  in  a 
part  of  his  labors.  Galileo,  an  Italian  astronomer  of 
great  eminence,  flourished  only  a  little  later  than  Tycho 
Brahe.  He  invented  the  telescope,  and,  both  by  his 
discoveries  and  reasonings,  contributed  greatly  to  estab- 
lish the  true  system  of  the  world.  Soon  after  the  com- 
mencement of  the  seventeenth  century,  (1620,)  Lord 


16  LETTERS  ON  ASTRONOMY. 

Bacon,  a  celebrated  English  philosopher,  pointed  out 
the  true  method  of  conducting  all  inquiries  into  the 
phenomena  of  Nature,  and  introduced  the  inductive 
method  of  philosophizing.  According  to  the  inductive 
method,  we  are  to  begin  our  inquiries  into  the  causes 
of  any  events  by  first  examining  and  classifying  all  the 
facts  that  relate  to  it,  and,  from  the  comparison  of  these, 
to  deduce  our  conclusions. 

But  the  greatest  single  discovery,  that  has  ever  been 
made  in  astronomy,  was  the  law  of  universal  gravitation, 
a  discovery  made  by  Sir  Isaac  Newton,  in  the  latter 
part  of  the  seventeenth  century.  The  discovery  of  this 
law  made  us  acquainted  with  the  hidden  forces  that 
move  the  great  machinery  of  the  universe.  It  furnished 
the  key  which  unlocks  the  inner  temple  of  Nature ;  and 
from  this  time  we  may  regard  astronomy  as  fixed  on  a 
sure  and  immovable  basis.  I  shall  hereafter  endeavor 
to  explain  to  you  the  leading  principles  of  universal 
gravitation,  when  we  come  to  the  proper  place  for  in- 
quiring into  the  causes  of  the  celestial  motions,  as  ex- 
emplified in  the  motion  of  the  earth  around  the  sun. 


LETTER  II. 

DOCTRINE  OF  THE  SPHERE. 

"  All  are  but  parts  of  one  stupendous  whole, 
Whose  body  Nature  is,  and  God  the  soul." — Pope. 

LET  us  now  consider  what  astronomy  is,  and  into 
what  great  divisions  it  is  distributed ;  and  then  we  will 
take  a  cursory  view  of  the  doctrine  of  the  sphere.  This 
subject  will  probably  be  less  interesting  to  you  than 
many  that  are  to  follow ;  but  still,  permit  me  to  urge 
upon  you  the  necessity  of  studying  it  with  attention, 
and  reflecting  upon  each  definition,  until  you  fully  un- 
derstand it ;  for,  unless  you  fully  and  clearly  compre- 
hend the  circles  of  the  sphere,  and  the  use  that  is  made 


DOCTRINE   OF  THE   SPHERE.  17 

of  them  in  astronomy,  a  mist  will  hang  over  every  sub- 
sequent portion  of  the  science.  I  beg  you,  therefore,  to 
pause  upon  every  paragraph  of  this  Letter  ;  and  if  there 
is  any  point  in  the  whole  which  you  cannot  clearly  un- 
derstand, I  would  advise  you  to  mark  it,  and  to  recur 
to  it  repeatedly  ;  and,  if  you  finally  cannot  obtain  a  clear 
idea  of  it  yourself,  I  would  recommend  to  you  to  apply 
for  aid  to  some  of  your  friends,  who  may  be  able  to  as- 
sist you. 

Astronomy  is  that  science  which  treats  of  the  heav- 
enly bodies.  More  particularly,  its  object  is  to  teach 
what  is  known  respecting  the  sun,  moon,  planets,  com- 
ets, and  fixed  stars  ;  and  also  to  explain  the  methods  by 
which  this  knowledge  is  acquired.  Astronomy  is  some- 
times divided  into  descriptive,  physical,  and  practical. 
Descriptive  astronomy  respects  facts;  physical  astrono- 
my, causes ;  practical  astronomy,  the  means  of  investi- 
gating the  facts,  whether  by  instruments  or  by  calcu- 
lation. It  is  the  province  of  descriptive  astronomy  to 
observe,  classify,  and  record,  all  the  phenomena  of  the 
heavenly  bodies,  whether  pertaining  to  those  bodies  in- 
dividually, or  resulting  from  their  motions  and  mutual 
relations.  It  is  the  part  of  physical  astronomy  to  ex- 
plain the  causes  of  these  phenomena,  by  investigating 
the  general  laws  on  which  they  depend ;  especially,  by 
tracing  out  all  the  consequences  of  the  law  of  universal 
gravitation.  Practical  astronomy  lends  its  aid  to  both 
the  other  departments. 

The  definitions  of  the  different  lines,  points,  and 
circles,  which  are  used  in  astronomy,  and  the  proposi- 
tions founded  upon  them,  compose  the  doctrine  of  the 
sphere.  Before  these  definitions  are  given,  I  must  re- 
call to  your  recollection  a  few  particulars  respecting  the 
method  of  measuring  angles.  (See  Fig.  1,  page  18.) 

A  line  drawn  from  the  centre  to  the  circumference 
of  a  circle  is  called  a  radius,  as  C  D,  C  B,  or  C  K. 

Any  part  of  the  circumference  of  a  circle  is  called  an 
arc,  as  A  B,  or  B  D. 

An  angle  is  measured  by  an  arc  included  between 
2* 


18 


LETTERS  ON  ASTRONOMY. 


two  radii.  Thus,  in  Fig. 
1,  the  angle  contained  be- 
tween the  two  radii,  C  A 
and  C  B,  that  is,  the  angle 
A  C  B,  is  measured  by  the 
arc  A  B.  Every  circle,  it 
will  be  recollected,  is  divi- 
ded into  three  hundred  and 
sixty  equal  parts,  called  de- 
grees ;  and  any  arc,  as  A  B, 
contains  a  certain  number 
of  degrees,  according  to 
its  length.  Thus,  if  the  arc  A  B  contains  forty  de- 
grees, then  the  opposite  angle  A  C  B  is  said  to  be  an 
angle  of  forty  degrees,  and  to  be  measured  by  A  B. 
But  this  arc  is  the  same  part  of  the  smaller  circle  that 
E  F  is  of  the  greater.  The  arc  A  B,  therefore,  con- 
tains the  same  number  of  degrees  as  the  arc  E  F,  and 
either  may  be  taken  as  the  measure  of  the  angle  A  C  B. 
As  the  whole  circle  contains  three  hundred  and  sixty  de- 
grees, it  is  evident,  that  the  quarter  of  a  circle,  or  quad- 
rant, contains  ninety  degrees,  and  that  the  semicircle 
A  B  D  G  contains  one  hundred  and  eighty  degrees. 

The  complement  of  an  arc,  or  angle,  is  what  it  wants 
of  ninety  degrees.  Thus,  since  A  D  is  an  arc  of  nine- 
ty degrees,  B  D  is  the  complement  of  A  B,  and  A  B  is 
the  complement  of  B  D.  If  A  B  denotes  a  certain 
number  of  degrees  of  latitude,  B  D  will  be  the  comple- 
ment of  the  latitude,  or  the  colatitude,  as  it  is  commonly 
written. 

The  supplement  of  an  arc,  or  angle,  is  what  it  wants 
of  one  hundred  and  eighty  degrees.  Thus,  B  A  is  the 
supplement  of  G  D  B,  and  G  D  B  is  the  supplement  of 
B  A.  If  B  A  were  twenty  degrees  of  longitude,  G  D  B, 
its  supplement,  would  be  one  hundred  and  sixty  de- 
grees. An  angle  is  said  to  be  subtended  by  the  side 
which  is  opposite  to  it.  Thus,  in  the  triangle  A  C  K, 
the  angle  at  C  is  subtended  by  the  side  A  K,  the  angle 
at  A  by  C  K,  and  the  angle  at  K  by  C  A.  In  like  man- 


DOCTRINE  OF  THE  SPHERE.  19 

ner,  a  side  is  said  to  be  subtended  by  an  angle,  as  A  K 
by  the  angle  at  C. 

Let  us  now  proceed  with  the  doctrine  of  the  sphere. 

A  section  of  a  sphere,  by  a  plane  cutting  it  in  any 
manner,  is  a  circle.  Great  circles  are  those  which  pass 
through  the  centre  of  the  sphere,  and  divide  it  into. two 
equal  hemispheres.  Small  circles  are  such  as  do  not 
pass  through  the  centre,  but  divide  the  sphere  into  two 
unequal  parts.  The  axis  of  a  circle  is  a  straight  line 
passing  through  its  centre  at  right  angles  to  its  plane. 
The  pole  of  a  great  circle  is  the  point  on  the  sphere 
where  its  axis  cuts  through  the  sphere.  Every  great 
circle  has  two  poles,  each  of  which  is  every  where  nine- 
ty degrees  from  the  great  circle.  All  great  circles  of 
the  sphere  cut  each  other  in  two  points  diametrically 
opposite,  and  consequently  their  points  of  section  are 
one  hundred  and  eighty  degrees  apart.  A  great  circle, 
which  passes  through  the  pole  of  another  great  circle, 
cuts  the  latter  at  right  angles.  The  great  circle  which 
passes  through  the  pole  of  another  great  circle,  and  is 
at  right  angles  to  it,  is  called  a  secondary  to  that 
circle.  The  angle  made  by  two  great  circles  on  the 
surface  of  the  sphere  is  measured  by  an  arc  of  an- 
other great  circle,  of  which  the  angular  point  is  the 
pole,  being  the  arc  of  that  great  circle  intercepted  be- 
tween those  two  circles. 

In  order  to  fix  the  position  of  any  place,  either  on 
the  surface  of  the  earth  or  in  the  heavens,  both  the 
earth  and  the  heavens  are  conceived  to  be  divided  into 
separate  portions,  by  circles,  which  are  imagined  to  cut 
through  them,  in  various  ways.  The  earth  thus  inter- 
sected is  called  the  terrestrial,  and  the  heavens  the  ce- 
lestial, sphere.  We  must  bear  in  mind,  that  these  cir- 
cles have  no  existence  in  Nature,  but  are  mere  land- 
marks, artificially  contrived  for  convenience  of  refer- 
ence. On  account  of  the  immense  distances  of  the 
heavenly  bodies,  they  appear  to  us,  wherever  we  are 
placed,  to  be  fixed  in  the  same  concave  surface,  or  ce- 
lestial vault.  The  great  circles  of  the  globe,  extended 


20  LETTERS  ON  ASTRONOMY. 

every  way  to  meet  the  concave  sphere  of  the  heavens, 
become  circles  of  the  celestial  sphere. 

The  horizon  is  the  great  circle  which  divides  the 
earth  into  upper  and  lower  hemispheres,  and  separates 
the  visible  heavens  from  the  invisible.  This  is  the  ra- 
tional horizon.  The  sensible  horizon  is  a  circle  touch- 
ing the  earth  at  the  place  of  the  spectator,  and  is  bound- 
ed by  the  line  in  which  the  earth  and  skies  seem  to 
meet.  The  sensible  horizon  is  parallel  to  the  rational, 
but  is  distant  from  it  by  the  semidiameter  of  the  earth, 
or  nearly  four  thousand  miles.  Still,  so  vast  is  the  dis- 
tance of  the  starry  sphere,  that  both  these  planes  ap- 
pear to  cut  the  sphere  in  the  same  line  ;  so  that  we  see 
the  same  hemisphere  of  stars  that  we  should  see,  if  the 
upper  half  of  the  earth  were  removed,  and  we  stood  on 
the  rational  horizon. 

The  poles  of  the  horizon  are  the  zenith  and  nadir. 
The  zenith  is  the  point  directly  over  our  heads ;  and 
the  nadir,  that  directly  under  our  feet.  The  plumb- 
line  (such  as  is  formed  by  suspending  a  bullet  by  a 
string)  is  in  the  axis  of  the  horizon,  and  consequently 
directed  towards  its  poles.  Every  place  on  the  surface 
of  the  earth  has  its  own  horizon  ;  and  the  traveller  has 
a  new  horizon  at  every  step,  always  extending  ninety 
degrees  from  him,  in  all  directions. 

Vertical  circles  are  those  which  pass  through  the  poles 
of  the  horizon,  (the  zenith  and  nadir,)  perpendicular  to  it. 

The  meridian  is  that  vertical  circle  which  passes 
through  the  north  and  south  points. 

The  prime  vertical  is  that  vertical  circle  which,pas- 
ses  through  the  east  and  west  points. 

The  altitude  of  a  body  is  its  elevation  above  the  ho- 
rizon, measured  on  a  vertical  circle. 

The  azimuth  of  a  body  is  its  distance,  measured  on 
the  horizon,  from  the  meridian  to  a  vertical  circle  pass- 
ing through  that  body. 

The  amplitude  of  a  body  is  its  distance,  on  the  ho- 
rizon, from  the  prime  vertical  to  a  vertical  circle  pass- 
ing through  the  body. 


DOCTRINE  OF  THE   SPHERE.  21 

Azimuth  is  reckoned  ninety  degrees  from  either  the 
north  or  south  point ;  and  amplitude  ninety  degrees 
from  either  the  east  or  west  point.  Azimuth  and  am- 
plitude are  mutually  complements  of  each  other,  for 
one  makes  up  what  the  other  wants  of  ninety  degrees. 
When  a  point  is  on  the  horizon,  it  is  only  necessary 
to  count  the  number  of  degrees  of  the  horizon  between 
that  point  and  the  meridian,  in  order  to  find  its  azi- 
muth ;  but  if  the  point  is  above  the  horizon,  then  its 
azimuth  is  estimated  by  passing  a  vertical  circle  through 
it,  and  reckoning  the  azimuth  from  the  point  where 
this  circle  cuts  the  horizon. 

The  zenith  distance  of  a  body  is  measured  on  a  ver- 
tical circle  passing  through  that  body.  It  is  the  com- 
plement of  the  altitude. 

The  axis  of  the  earth  is  the  diameter  on  which  the 
earth  is  conceived  to  turn  in  its  diurnal  revolution. 
The  same  line,  continued  until  it  meets  the  starry  con- 
cave, constitutes  the  axis  of  the  celestial  sphere. 

The  poles  of  the  earth  are  the  extremities  of  the 
earth's  axis :  the  poles  of  the  heavens,  the  extremities 
of  the  celestial  axis. 

The  equator  is  a  great  circle  cutting  the  axis  of  the 
earth  at  right  angles.  Hence,  the  axis  of  the  earth  is 
the  axis  of  the  equator,  and  its  poles  are  the  poles  of 
the  equator.  The  intersection  of  the  plane  of  the  equa- 
tor with  the  surface  of  the  earth  constitutes  the  terres- 
trial, and  its  intersection  with  the  concave  sphere  of 
the  heavens,  the  celestial.,  equator.  The  latter,  by  way 
of  distinction,  is  sometimes  denominated  the  equinoctial. 

T?te  secondaries  to  the  equator, — that  is,  the  great 
circles  passing  through  the  poles  of  the  equator, — are 
called  meridians,  because  that  secondary  which  passes 
through  the  zenith  of  any  place  is  the  meridian  of  that 
place,  and  is  at  right  angles  both  to  the  equator  and 
the  horizon,  passing,  as  it  does,  through  the  poles  of 
both.  These  secondaries  are  also  called  hour  circles^ 
because  the  arcs  of  the  equator  intercepted  between 
them  are  used  as  measures  of  time. 


LETTERS  ON  ASTRONOMY. 

The  latitude  of  a  place  on  the  earth  is  its  distance 
from  the  equator  north  or  south.  The  polar  distance, 
or  angular  distance  from  the  nearest  pole,  is  the  com- 
plement of  the  latitude. 

The  longitude  of  a  place  is  its  distance  from  some 
standard  meridian,  either  east  or  west,  measured  on  the 
equator.  The  meridian,  usually  taken  as  the  standard, 
is  that  of  the  Observatory  of  Greenwich,  in  London. 
If  a  place  is  directly  on  the  equator,  we  have  only  to 
inquire,  how  many  degrees  of  the  equator  there  are  be- 
tween that  place  and  the  point  where  the  meridian  of 
Greenwich  cuts  the  equator.  If  the  place  is  north  or 
south  of  the  equator,  then  its  longitude  is  the  arc  of  the 
equator  intercepted  between  the  meridian  which  passes 
through  the  place  and  the  meridian  of  Greenwich. 

The  ecliptic  is  a  great  circle,  in  which  the  earth 
performs  its  annual  revolutions  around  the  sun.  It 
passes  through  the  centre  of  the  earth  and  the  centre 
of  the  sun.  It  is  found,  by  observation,  that  the  earth 
does  not  lie  with  its  axis  at  right  angles  to  the  plane  of 
the  ecliptic,  so  as  to  make  the  equator  coincide  with  it. 
but  that  it  is  turned  about  twenty-three  and  a  half  de- 
grees out  of  a  perpendicular  direction,  making  an  angle 
with  the  plane  itself  of  sixty-six  and  a  half  degrees. 
The  equator,  therefore,  must  be  turned  the  same  dis- 
tance out  of  a  coincidence  with  the  ecliptic,  the  two 
circles  making  an  angle  with  each  other  of  twenty- 
three  and  a  half  degrees.  It  is  particularly  important 
that  we  should  form  correct  ideas  of  the  ecliptic,  and 
of  its  relations  t .  the  equator,  since  to  these  two  cir- 
cles a  great  number  of  astronomical  measurements  and 
phenomena  are  referred. 

The  equinoctial  points,  or  equinoxes,  are  the  inter- 
sections of  the  ecliptic  and  equator.  The  time  when 
the  sun  crosses  the  equator,  in  going  northward,  is  call- 
ed the  vernal,  and  in  returning  southward,  the  autum- 
nal, equinox.  The  vernal  equinox  occurs  about  the 
twenty-first  of  March,  and  the  autumnal,  about  the 
twenty-second  of  September. 


DOCTRINE  OF  THE   SPHERE.  23 

The  solstitial  points  are  the  two  points  of  the  eclip- 
tic most  distant  from  the  equator.  The  times  when 
the  sun  comes  to  them  are  called  solstices.  The  Sum- 
mer solstice  occurs  about  the  twenty-second  of  June, 
and  the  Winter  solstice  about  the  twenty-second  of 
December.  The  ecliptic  is  divided  into  twelve  equal 
parts,  of  thirty  degrees  each,  called  signs,  which,  be- 
ginning at  the  vernal  equinox,  succeed  each  other,  in 
the  following  order : 

1.  Aries,  °f»  7.  Libra,  =s= 

2.  Taurus,         y  8.  Scorpio,          TH. 

3.  Gemini,        n  9.  Sagittarius,      / 

4.  Cancer,        Z5  10.  Capricornus,  vj 

5.  Leo,  SI  11.  Aquarius,       *# 

6.  Virgo,  TIK  12.  Pisces.  X 
The  mode  of  reckoning  on  the  ecliptic  is  by  signs, 

degrees,  minutes,  and  seconds.  The  sign  is  denoted 
either  by  its  name  or  its  number.  Thus,  one  hundred 
degrees  may  be  expressed  either  as  the  tenth  degree  of 
Cancer,  or  as  3s  10°.  It  will  be  found  an  advantage 
to  repeat  the  signs  in  their  proper  order,  until  they  are 
well  fixed  in  the  memory,  and  to  be  able  to  recognise 
each  sign  by  its  appropriate  character. 

Of  the  various  meridians,  two  are  distinguished  by 
the  name  of  colures.  The  equinoctial  colure  is  the 
meridian  which  passes  through  the  equinoctial  points. 
From  this  meridian,  right  ascension  and  celestial  longi- 
tude are  reckoned,  as  longitude  on  the  earth  is  reckon- 
ed from  the  meridian  of  Greenwich.  The  solstitial 
colure  is  the  meridian  which  passes  through  the  sol- 
stitial points. 

The  position  of  a  celestial  body  is  referred  to  the 
equator  by  its  right  ascension  and  declination.  Right 
ascension  is  the  angular  distance  from  the  vernal  equi- 
nox measured  on  the  equator.  If  a  star  is  situated  on 
the  equator,  then  its  right  ascension  is  the  number  of 
degrees  of  the  equator  between  the  star  and  the  vernal 
equinox.  But  if  the  star  is  north  or  south  of  the  equa- 
tor, then  its  right  ascension  is  the  number  of  degrees  of 


24  LETTERS  ON  ASTRONOMY. 

the  equator,  intercepted  between  the  vernal  equinox 
and  that  secondary  to  the  equator  which  passes  through 
the  star.  Declination  is  the  distance  of  a  body  from 
the  equator  measured  on  a  secondary  to  the  latter. 
Therefore,  right  ascension  and  declination  correspond 
to  terrestrial  longitude  and  latitude, — right  ascension 
being  reckoned  from  the  equinoctial  colure,  in  the  same 
manner  as  longitude  is  reckoned  from  the  meridian  of 
Greenwich.  On  the  other  hand,  celestial  longitude 
and  latitude  are  referred,  not  to  the  equator,  but  to  the 
ecliptic.  Celestial  longitude  is  the  distance  of  a  body 
from  the  vernal  equinox  measured  on  the  ecliptic.  Ce- 
lestial latitude  is  the  distance  from  the  ecliptic  meas- 
ured on  a  secondary  to  the  latter.  Or,  more  briefly, 
longitude  is  distance  on  the  ecliptic :  latitude,  distance 
from  the  ecliptic.  The  north  polar  distance  of  a  star 
is  the  complement  of  its  declination. 

Parallels  of  latitude  are  small  circles  parallel  to  the 
equator.  They  constantly  diminish  in  size,  as  we  go 
from  the  equator  to  the  pole.  The  tropics  are  the  par- 
allels of  latitude  which  pass  through  the  solstices.  The 
northern  tropic  is  called  the  tropic  of  Cancer  ;  the  south- 
ern, the  tropic  of  Capricorn.  The  polar  circles  are  the 
parallels  of  latitude  that  pass  through  the  poles  of  the 
ecliptic,  at  the  distance  of  twenty-three  and  a  half  de- 
grees from  the  poles  of  the  earth. 

The  elevation  of  the  pole  of  the  heavens  above  the 
horizon  of  any  place  is  always  equal  to  the  latitude  of 
the  place.  Thus,  in  forty  degrees  of  north  latitude  we 
see  the  north  star  forty  degrees  above  the  northern  ho- 
rizon ;  whereas,  if  we  should  travel  southward,  its  ele- 
vation would  grow  less  and  less,  until  we  reached  the 
equator,  where  it  would  appear  in  the  horizon.  Or,  if 
we  should  travel  northwards,  the  north  star  would  rise 
continually  higher  and  higher,  until,  if  we  could  reach 
the  pole  of  the  earth,  that  star  would  appear  directly 
over  head.  The  elevation  of  the  equator  above  the 
horizon  of  any  place  is  equal  to  the  complement  of 
the  latitude.  Thus,  at  the  latitude  of  forty  degrees 


DOCTRINE  OF  THE  SPHERE.  25 

north,  the  equator  is  elevated  fifty  degrees  above  the 
southern  horizon. 

The  earth  is  divided  into  five  zones.  That  portion 
of  the  earth  which  lies  between  the  tropics  is  called 
the  torrid  zone ;  that  between  the  tropics  and  the  po- 
lar circles,  the  temperate  zones  ;  and  that  between  the 
polar  circles  and  the  poles,  the  frigid  zones. 

The  zodiac  is  the  part  of  the  celestial  sphere  which 
lies  about  eight  degrees  on  each  side  of  the  eclip- 
tic. This  portion  of  the  heavens  is  thus  marked  off  by 
itself,  because  all  the  planets  move  within  it. 

After  endeavoring  to  form,  from  the  definitions,  as 
clear  an  idea  as  we  can  of  the  various  circles  of  the 
sphere,  we  may  next  resort  to  an  artificial  globe,  and 
see  how  they  are  severally  represented  there.  I  do  not 
advise  to  begin  learning  the  definitions  from  the  globe  ; 
the  mind  is  more  improved,  and  a  power  of  conceiving 
clearly  how  things  are  in  Nature  is  more  effectually  ac- 
quired, by  referring  every  thing,  at  first,  to  the  grand 
sphere  of  Nature  itself,  and  afterwards  resorting  to  ar- 
tificial representations  to  aid  our  conceptions.  We  can 
get  but  a  very  imperfect  idea  of  a  man  from  a  profile 
cut  in  paper,  unless  we  know  the  original.  If  we  are 
acquainted  with  the  individual,  the  profile  will  assist  us 
to  recall  his  appearance  more  distinctly  than  we  can  do 
without  it.  In  like  manner,  orreries,  globes,  and  other 
artificial  *aids,  will  be  found  very  useful,  in  assisting  us 
to  form  distinct  conceptions  of  the  relations  existing  be- 
tween the  different  circles  of  the  sphere,  and  of  the 
arrangements  of  the  heavenly  bodies ;  but,  unless  we 
have  already  acquired  some  correct  ideas  of  these 
things,  by  contemplating  them  as  they  are  in  Nature, 
artificial  globes,  and  especially  orreries,  will  be  apt  to 
mislead  us. 

I  trust  you  will  be  able  to  obtain  the  use  of  a  globe,* 

*  A  small  pair  of  globes,  that  will  answer  every  purpose  required 
by  the  readers  of  these  Letters,  may  be  had  of  the  publishers  of  this 
Work,  at  a  price  not  exceeding  ten  dollars  ;  or  half  that  sum  for  a 
celestial  globe,  which  will  serve  alone  for  studying  astronomy. 
3  L.  A. 


26  LETTERS  ON  ASTRONOMY. 

i 

to  aid  you  in  the  study  of  the  foregoing  definitions,  or 
doctrine  of  the  sphere  ;  but  if  not,  I  would  recommend 
the  following  easy  device.  To  represent  the  earth, 
select  a  large  apple,  (a  melon,  when  in  season,  will  be 
found  still  better.)  The  eye  and  the  stem  of  the  ap- 
ple will  indicate  the  position  of  the  two  poles  of  the 
earth.  Applying  the  thumb  and  finger  of  the  left  hand 
to  the  poles,  and  holding  the  apple  so  that  the  poles 
may  be  in  a  north  and  south  line,  turn  this  globe  from 
west  to  east,  and  its  motion  will  correspond  to  the  di- 
urnal movement  of  the  earth.  Pass  a  wire  or  a  knit- 
ting needle  through  the  poles,  and  it  will  represent  the 
axis  of  the  sphere.  A  circle  cut  around  the  apple,  half 
way  between  the  poles,  will  be  the  equator ;  and  sev- 
eral other  circles  cut  between  the  equator  and  the  poles, 
parallel  to  the  equator,  will  represent  parallels  of  lati- 
tude ;  of  which,  two,  drawn  twenty-three  and  a  half  de- 
grees from  the  equator,  will  be  the  tropics,  and  two 
others,  at  the  same  distance  from  the  poles,  will  be  the 
polar  circles.  A  great  circle  cut  through  the  poles,  in 
a  north  and  south  direction,  will  form  the  meridian, 
and  several  other  great  circles  drawn  through  the  poles, 
and  of  course  perpendicularly  to  the  equator,  will  be 
secondaries  to  the  equator,  constituting  meridians,  or 
hour  circles.  A  great  circle  cut  through  the  centre  of 
the  earth,  from  one  tropic  to  the  other,  would  represent 
the  plane  of  the  ecliptic ;  and  consequently  a  line  cut 
round  the  apple  where  such  a  section  meets  the  sur- 
face, will  be  the  terrestrial  ecliptic.  The  points  where 
this  circle  meets  the  tropics  indicate  the  position  of  the 
solstices ;  and  its  intersection  with  the  equator,  that  of 
the  equinoctial  points. 

The  horizon  is  best  represented  by  a  circular  piece 
of  pasteboard,  cut  so  as  to  fit  closely  to  the  apple,  be- 
ing movable  upon  it.  When  this  horizon  is  passed 
through  the  poles,  it  becomes  the  horizon  of  the  equa- 
tor ;  when  it  is  so  placed  as  to  coincide  with  the  earth's 
equator,  it  becomes  the  horizon  of  the  poles ;  and  in 
every  other  situation  it  represents  the  horizon  of  a 


DOCTRINE   OF  THE   SPHERE.  27 

place  on  the  globe  ninety  degrees  every  way  from  it. 
Suppose  we  are  in  latitude  forty  degrees ;  then  let  us 
place  our  movable  paper  parallel  to  our  own  horizon, 
and  elevate  the  pole  forty  degrees  above  it,  as  near  as 
we  can  judge  by  the  eye.  If  we  cut  a  circle  around 
the  apple,  passing  through  its  highest  part,  and  through 
the  east  and  west  points,  it  will  represent  the  prime 
vertical. 

Simple  as  the  foregoing  device  is,  if  you  will  take 
the  trouble  to  construct  one  for  yourself,  it  will  lead 
you  to  more  correct  views  of  the  doctrine  of  the  sphere, 
than  you  would  be  apt  to  obtain  from  the  most  expen- 
sive artificial  globes,  although  there  are  many  other  use- 
ful purposes  which  such  globes  serve,  for  which  the  ap- 
ple would  be  inadequate.  When  you  have  thus  made 
a  sphere  for  yourself,  or,  with  an  artificial  globe  before 
you,  if  you  have  access  to  one,  proceed  to  point  out  on 
it  the  various  arcs  of  azimuth  and  altitude,  right  ascen- 
sion and  declination,  terrestrial  and  celestial  latitude 
and  longitude, — these  last  being  referred  to  the  equa- 
tor on  the  earth,  and  to  the  ecliptic  in  the  heavens. 

When  the  circles  of  the  sphere  are  well  learned,  we 
may  advantageously  employ  projections  of  them  in  va- 
rious illustrations.  By  the  projection  of  the  sphere  is 
meant  a  representation  of  all  its  parts  on  a  plane.  The 
plane  itself  is  called  the  plane  of  projection.  Let  us 
take  any  circular  ring,  as  a  wire  bent  into  a  circle,  and 
hold  it  in  different  positions  before  the  eye.  If  we  hold 
it  parallel  to  the  face,  with  the  whole  breadth  opposite 
to  the  eye,  we  see  it  as  an  entire  circle.  If  we  turn  it 
a  little  sideways,  it  appears  oval,  or  as  an  ellipse ;  and, 
as  we  continue  to  turn  it  more  and  more  round,  the 
ellipse  grows  narrower  and  narrower,  until,  when  the 
edge  is  presented  to  the  eye,  we  see  nothing  but  a  line. 
Now  imagine  the  ring  to  be  near  a  perpendicular  wall, 
and  the  eye  to  be  removed  at  such  a  distance  from  it, 
as  not  to  distinguish  any  interval  between  the  ring  and 
the  wall ;  then  the  several  figures  under  which  the  ring 
is  seen  will  appear  to  be  inscribed  on  the  wall,  and  we 


LETTERS  ON  ASTRONOMY. 


shall  see  the  ring  as  a  circle,  when  perpendicular  to  a 
straight  line  joining  the  centre  of  the  ring  and  the  eye, 
or  as  an  ellipse,  when  oblique  to  this  line,  or  as  a  straight 
line,  when  its  edge  is  towards  us. 

It  is  in  this  manner  that  the  circles  of  the  sphere  are 
projected,  as  represented  in  the  following  diagram,  Fig.  2. 

Here,  various  circles 
are  represented  as 
projected  on  the  me- 
ridian, which  is  sup- 
posed to  be  situated 
directly  before  the 
eye,  at  some  distance 
from  it.  The  horizon 
H  O,  being  perpendic- 
ular to  the  meridian, 
is  seen  edgewise^  and 
consequently  is  pro- 
jected into  a  straight 
line.  The  same  is  the 
case  with  the  prime  vertical  Z  N,  with  the  equator  E  Q, 
and  the  several  small  circles  parallel  to  the  equator, 
which  represent  the  two  tropics  and  the  two  polar  cir- 
cles. In  fact,  all  circles  whatsoever,  which  are  perpen- 
dicular to  the  plane  of  projection,  will  be  represented 
by  straight  lines.  But  every  circle  which  is  perpen- 
dicular to  the  horizon,  except  the  prime  vertical,  being 
seen  obliquely,  as  Z  M  N,  will  be  projected  into  an 
ellipse,  one  half  only  of  which  is  seen, — the  other  half 
being  on  the  other  side  of  the  plane  of  projection.  In 
the  same  manner,  P  R  P,  an  hour  circle,  is  represented 
by  an  ellipse  on  the  plane  of  projection. 


ASTRONOMICAL  INSTRUMENTS.  29 


LETTER  III. 

ASTRONOMICAL  INSTRUMENTS. TELESCOPB. 

"  Here  truths  sublime,  and  sacred  science  charm, 
Creative  arts  new  faculties  supply, 
Mechanic  powers  give  more  than  giant's  arm, 
And  piercing  optics  more  than  eagle's  eye; 
Eyes  that  explore  creation's  wondrous  laws, 
And  teach  us  to  adore  the  great  Designing  Cause." — Beattie. 

IF,  as  I  trust,  you  have  gained  a  clear  and  familiar 
knowledge  of  the  circles  and  divisions  of  the  sphere, 
and  of  the  mode  of  estimating  the  position  of  a  heav- 
enly body  by  its  azimuth  and  altitude,  or  by  its  right  as- 
cension and  declination,  or  by  its  longitude  and  latitude, 
you  will  now  enter  with  advantage  upon  an  account 
of  those  instruments,  by  means  of  which  our  knowl- 
edge of  astronomy  has  been  greatly  promoted  and  per- 
fected. 

The  most  ancient  astronomers  employed  no  instru- 
ments of  observation,  but  acquired  their  knowledge  of 
the  heavenly  bodies  by  long-continued  and  most  atten- 
tive inspection  with  the  naked  eye.  Instruments  for 
measuring  angles  were  first  used  in  the  Alexandrian 
school,  about  three  hundred  years  before  the  Christian 
era. 

Wherever  we  are  situated  on  the  earth,  we  appear  to 
be  in  the  centre  of  a  vast  sphere,  on  the  concave  sur- 
face of  which  all  celestial  objects  are  inscribed.  If  we 
take  any  two  points  on  the  surface  of  the  sphere,  as  two 
stars,  for  example,  and  imagine  straight  lines  to  be 
drawn  to  them  from  the  eye,  the  angle  included  be- 
tween these  lines  will  be  measured  by  the  arc  of  the 
sky  contained  between  the  two  points.  Thus,  if  D  B  H, 
Fig.  3,  page  30,  represents  the  concave  surface  of  the 
sphere,  A,  B,  two  points  on  it,  as  two  stars,  and  C  A, 
C  B,  straight  lines  drawn  from  the  spectator  to  those 
points,  then  the  angular  distance  between  them  is  meas- 
ured by  the  arc  A  B,  or  the  angle  A  C  B.  But  this  an* 
3* 


30  LETTERS  ON  ASTRONOMY. 

Fig.  3. 


gle  may  be  measured  on  a  much  smaller  circle,  having 
the  same  centre,  as  G  F  K,  since  the  arc  E  F  will  have 
the  same  number  of  degrees  as  the  arc  A  B.  The  sim- 
plest mode  of  taking  an  angle  between  two  stars  is  by 
means  of  an  arm  opening  at  a  joint  like  the  blade  of  a 
penknife,  the  end  of  the  arm  moving  like  C  E  upon  the 
graduated  circle  K  F  G.  In  fact,  an  instrument  con- 
structed on  this  principle,  resembling  a  carpenter's  rule 
with  a  folding  joint,  with  a  semicircle  attached,  consti- 
tuted the  first  rude  apparatus  for  measuring  the  angular 
distance  between  two  points  on  the  celestial  sphere. 
Thus  the  sun's  elevation  above  the  horizon  might  be 
ascertained,  by  placing  one  arm  of  the  rule  on  a  level 
with  the  horizon,  and  bringing  the  edge  of  the  other  in- 
to a  line  with  the  sun's  centre. 

The  common  surveyor's  compass  affords  a  simple 
example  of  angular  measurement.  Here,  the  needle 
lies  in  a  north  and  south  line,  while  the  circular  rim  of 
the  compass,  when  the  instrument  is  level,  corresponds 
to  the  horizon.  Hence  the  compass  shows  the  azimuth 
of  an  object,  or  how  many  degrees  it  lies  east  or  west 
of  the  meridian. 

It  is  obvious,  that  the  larger  the  graduated  circle  is, 
the  more  minutely  its  limb  may  be  divided.  If  the  cir- 
cle is  one  foot  in  diameter,  each  degree  will  occupy  one 
tenth  of  an  inch.  If  the  circle  is  twenty  feet  in  diame- 
ter, a  degree  will  occupy  the  space  of  two  inches,  and 
could  be  easily  divided  into  minutes,  since  each  minute 
would  cover  a  space  one  thirtieth  of  an  inch.  Refined 


TELESCOPE.  %  31 

astronomical  circles  are  now  divided  with  very  great 
skill  and  accuracy,  the  spaces  between  the  divisions  be- 
ing, when  read  off,  magnified  by  a  microscope ;  but  in 
former  times,  astronomers  had  no  mode  of  measuring 
small  angles  but  by  employing  very  large  circles.  But  the 
telescope  and  microscope  enable  us  at  present  to  meas- 
ure celestial  arcs  much  more  accurately  than  was  done 
by  the  older  astronomers.  In  the  best  instruments,  the 
measurements  extend  to  a  single  second  of  space,  or 
one  thirty-six  hundredth  part  of  a  degree, — a  space,  on  a 
circle  twelve  feet  in  diameter,  no  greater  than  one  fifty- 
seven  hundredth  part  of  an  inch.  To  divide,  or  gradu- 
ate, astronomical  instruments,  to  such  a  degree  of  nicety, 
requires  the  highest  efforts  of  mechanical  skill.  Indeed, 
the  whole  art  of  instrument-making  is  regarded  as  the 
most  difficult  and  refined  of  all  the  mechanical  arts ; 
and  a  few  eminent  artists,  who  have  produced  instru- 
ments of  peculiar  power  and  accuracy,  take  rank  with 
astronomers  of  the  highest  celebrity. 

I  will  endeavor  to  make  you  acquainted  with  several 
of  the  principal  instruments  employed  in  astronomical 
observations,  but  especially  with  the  telescope,  which  is 
the  most  important  and  interesting  of  them  all.  I  think 
I  shall  consult  your  wishes,  as  well  as  your  improve- 
ment, by  giving  you  a  clear  insight  into  the  principles 
of  this  prince  of  instruments,  and  by  reciting  a  few  par- 
ticulars, at  least,  respecting  its  invention  and  subsequent 
history. 

The  Telescope,  as  its  name  implies,  is  an  instrument 
employed  for  viewing  distant  objects.*  It  aids  the  eye 
in  two  ways ;  first,  by  enlarging  the  visual  angle  under 
which  objects  are  seen,  and,  secondly,  by  collecting  and 
conveying  to  the  eye  a  much  larger  amount  of  the  light 
that  emanates  from  the  object,  than  would  enter  the 
naked  pupil.  A  complete  knowledge  of  the  telescope 
cannot  be  acquired,  without  an  acquaintance  with  the 
science  of  optics ;  but  one  unacquainted  with  that  sci- 

*  From  two  Greek  words,  ri^e,  (tele,)  far,  and  oxonsm,  (skopeo,) 
to  see. 


32  LETTERS  ON  ASTRONOMY. 

ence  may  obtain  some  idea  of  the  leading  principles  of 
this  noble  instrument.  Its  main  principle  is  as  follows : 
By  means  of  the  telescope,  we  first  form  an  image  of 
a  distant  object, — as  the  moon,  for  example, — and 
then  magnify  that  image  by  a  microscope. 

Let  us  first  see  how  the  image  is  formed.  This  may 
be  done  either  by  a  convex  lens,  or  by  a  concave  mir- 
ror. A  convex  lens  is  a  flat  piece  of  glass,  having  its 
two  faces  convex,  or  spherical,  as  is  seen  in  a  common 
sun-glass,  or  a  pair  of  spectacles.  Every  one  who  has 
seen  a  sun-glass,  knows,  that,  when  held  towards  the 
sun,  it  collects  the  solar  rays  into  a  small  bright  circle 
in  the  focus.  This  is  in  fact  a  small  image  of  the  sun. 
In  the  same  manner,  the  image  of  any  distant  object,  as 
a  star,  may  be  formed,  as  is  represented  in  the  following 
diagram.  Let  A  B  C  D,  Fig.  4,  represent  the  tube  of 

Fig.  4. 


the  telescope.  At  the  front  end,  or  at  the  end  which 
is  directed  towards  the  object,  (which  we  will  suppose 
to  be  the  moon,)  is  inserted  a  convex  lens,  L,  which 
receives  the  rays  of  light  from  the  moon,  and  collects 
them  into  the  focus  at  a,  forming  an  image  of  the  moon. 
This  image  is  viewed  by  a  magnifier  attached  to  the 
end  B  C.  The  lens,  L,  is  called  the  object-glass,  and 
the  microscope  in  B  C,  the  eyeglass.  We  apply  a  mi- 
croscope to  this  image  just  as  we  would  to  any  object ; 
and,  by  greatly  enlarging  its  dimensions,  we  may  render 
its  various  parts  far  more  distinct  than  they  would  oth- 
erwise be ;  while,  at  the  same  time,  the  lens  collects 
and  conveys  to  the  eye  a  much  greater  quantity  of  light 


TELESCOPE.  33 

than  would  proceed  directly  from  the  body  under  ex- 
amination. A  very  few  rays  of  light  only,  from  a  dis- 
tant object,  as  a  star,  can  enter  the  eye  directly ;  but  a 
lens  one  foot  in  diameter  will  collect  a  beam  of  light  of 
the  same  dimensions,  and  convey  it  to  the  eye.  By 
these  means,  many  obscure  celestial  objects  become 
distinctly  visible,  which  would  otherwise  be  either  too 
minute,  or  not  sufficiently  luminous,  to  be  seen  by  us. 

But  the  image  may  also  be  formed  by  means  of  a 
concave  mirror,  which,  as  well  as  the  concave  lens,  has 
the  property  of  collecting  the  rays  of  light  which  pro- 
ceed from  any  luminous  body,  and  of  forming  an  image 
of  that  body.  The  image  formed  by  a  concave  mirror 
is  magnified  by  a  microscope,  in  the  same  manner  as 
when  formed  by  the  concave  lens.  When  the  lens  is 
used  to  form  an  image,  the  instrument  is  called  a  re- 
fracting  telescope ;  when  a  concave  mirror  is  used,  it 
is  called  a  reflecting  telescope. 

The  office  of  the  object-glass  is  simply  to  collect  th^ 
light,  and  to  form  an  image  of  the  object,  but  not  to 
magnify  it :  the  magnifying  power  is  wholly  in  the  eye- 
glass. Hence  the  principle  of  the  telescope  is  as  fol- 
lows :  By  means  of  the  object-glass,  (in  the  refracting 
telescope,)  or  by  the  concave  mirror,  (in  the  reflecting 
telescope,)  we  form  an  image  of  the  object,  and  mag- 
nify that  image  by  a  microscope. 

The  invention  of  this  noble  instrument  is  generally 
ascribed  to  the  great  philosopher  of  Florence,  Galileo. 
He  had  heard  that  a  spectacle  maker  of  Holland  had 
accidentally  hit  upon  a  discovery,  by  which  distant  ob- 
jects might  be  brought  apparently  nearer ;  and,  without 
further  information,  he  pursued  the  inquiry,  in  order  to 
ascertain  what  forms  and  combinations  of  glasses  would 
produce  such  a  result.  By  a  very  philosophical  process 
of  reasoning,  he  was  led  to  the  discovery  of  that  pecu- 
liar form  of  the  telescope  which  bears  his  name. 

Although  the  telescopes  made  by  Galileo  were  no 
larger  than  a  common  spy-glass  of  the  kind  now  used 
on  board  of  ships,  yet,  as  they  gave  new  views  of  the 


34  LETTERS  ON  ASTRONOMY. 

heavenly  bodies,  revealing  the  mountains  and  valleys 
of  the  moon,  the  satellites  of  Jupiter,  and  multitudes  of 
stars  which  are  invisible  to  the  naked  eye,  it  was  re- 
garded with  infinite  delight  and  astonishment. 

Reflecting  telescopes  were  first  constructed  by  Sir 
Isaac  Newton,  although  the  use  of  a  concave  reflector, 
instead  of  an  object-glass,  to  form  the  image,  had  been 
previously  suggested  by  Gregory,  an  eminent  Scotch  as- 
tronomer. The  first  telescope  made  by  Newton  was  only 
six  inches  long.  Its  reflector,  too,  was  only  a  little  more 
than  an  inch.  Notwithstanding  its  small  dimensions, 
it  performed  so  well,  as  to  encourage  further  efforts ; 
and  this  illustrious  philosopher  afterwards  constructed 
much  larger  instruments,  one  of  which,  made  with  his 
own  hands,  was  presented  to  the  Royal  Society  of  Lon- 
don, and  is  now  carefully  preserved  in  their  library. 

Newton  was  induced  to  undertake  the  construction 
of  reflecting  telescopes,  from  the  belief  that  refracting 
telescopes  were  necessarily  limited  to  a  very  small  size, 
with  only  moderate  illuminating  powers,  whereas  the 
dimensions  and  powers  of  the  former  admitted  of  being 
indefinitely  increased.  Considerable  magnifying  pow- 
ers might,  indeed,  be  obtained  from  refractors,  by  mak- 
ing them  very  long ;  but  the  brightness  with  which 
telescopic  objects  are  seen,  depends  greatly  on  the 
dimensions  of  the  beam  of  light  which  is  collected  by 
the  object-glass,  or  by  the  mirror,  and  conveyed  to  the 
eye ;  asd  therefore,  small  object-glasses  cannot  have  a 
very  high  illuminating  power.  Now,  the  experiments 
of  Newton  on  colors  led  him  to  believe,  that  it  would  be 
impossible  to  employ  large  lenses  in  the  construction  of 
telescopes,  since  such  glasses  would  give  to  the  images, 
they  formed,  the  colors  of  the  rainbow.  But  later  opti- 
cians have  found  means  of  correcting  these  imperfec- 
tions, so  that  we  are  now  able  to  use  object-glasses  a  foot 
or  more  in  diameter,  which  give  very  clear  and  bright 
images.  Such  instruments  are  called  achromatic  tele- 
scopes,— a  name  implying  the  absence  of  prismatic  or 
rainbow  colors  in  the  image. '  It  is,  however,  far  more 


TELESCOPE.  35 

difficult  to  construct  large  achromatic  than  large  reflect- 
ing telescopes.  Very  large  pieces  of  glass  can  seldom 
be  found,  that  are  sufficiently  pure  for  the  purpose ; 
since  every  inequality  in  the  glass,  such  as  waves,  tears, 
threads,  and  the  like,  spoils  it  for  optical  purposes,  as 
it  distorts  the  light,  and  produces  nothing  but  confused 
images. 

The  achromatic  telescope  (that  is,  the  refracting  tel- 
escope, having  such  an  object-glass  as  to  give  a  colorless 
image)  was  invented  by  Dollond,  a  distinguished  Eng- 
lish artist,  about  the  year  1757.  He  had  in  his  posses- 
sion a  quantity  of  glass  of  a  remarkably  fine  quality, 
which  enabled  him  to  carry  his  invention  at  once  to  a 
high  degree  of  perfection.  It  has  ever  since  been,  with 
the  manufacturers  of  telescopes,  a  matter  of  the  greatest 
difficulty  to  find  pieces  of  glass,  of  a  suitable  quality  for 
object-glasses,  more  than  two  or  three  inches  in  di- 
ameter. Hence,  large  achromatic  telescopes  are  very 
expensive,  being  valued  in  proportion  to  the  cubes  of 
their  diameters ;  that  is,  if  a  telescope  whose  aperture 
(as  the  breadth  of  the  object-glass  is  technically  called) 
is  two  inches,  cost  one  hundred  dollars,  one  whose  aper- 
ture is  eight  inches  would  cost  six  thousand  four  hun- 
dred dollars. 

Since  it  is  so  much  easier  to  make  large  reflecting 
than  large  refracting  telescopes,  you  may  ask,  why  the 
latter  are  ever  attempted,  and  why  reflectors  are  not 
exclusively  employed  ?  I  answer,  that  the  achromatic 
telescope,  when  large  and  well  constructed,  is  a  more 
perfect  and  more  durable  instrument  than  the  reflecting 
telescope.  Much  more  of  the  light  that  falls  on  the 
mirror  is  absorbed  than  is  lost  in  passing  through  the 
object-glass  of  a  refractor ;  and  hence  the  larger  achro- 
matic telescopes  afford  a  stronger  light  than  the  reflect- 
ing, unless  the  latter  are  made  of  an  enormous  and  un- 
wieldy size.  Moreover,  the  mirror  is  very  liable  to 
tarnish,  and  will  never  retain  its  full  lustre  for  many 
years  together ;  and  it  is  no  easy  matter  to  restore  the 
lustre,  when  once  impaired. 


36  LETTERS  ON  ASTRONOMY. 

In  my  next  Letter,  I  will  give  you  an  account  of 
some  of  the  most  celebrated  telescopes  that  have  ever 
been  constructed,  and  point  out  the  method  of  using 
this  excellent  instrument,  so  as  to  obtain  with  it  the 
finest  views  of  the  heavenly  bodies. 


LETTER  IV. 


TELESCOPE  CONTINUED. 


the  broad  circumference 


Hung  on  his  shoulders  like  the  moon,  whose  orb 

Through  optic  glass  the  Tuscan  artist  views 

At  evening,  from  the  top  of  Fesole' 

Or  in  Valdarno,  to  descry  new  lands, 

Rivers  or  mountains,  in  her  spotted  globe." — Milton. 

,  THE  two  most  celebrated  telescopes,  hitherto  made, 
are  HerscheYs  forty-feet  reflector,  and  the  great  Dorpat 
refractor.  Herschel  was  a  Hanoverian  by  birth,  but 
settled  in  England  in  the  younger  part  of  his  life. 
As  early  as  1774,  he  began  to  make  telescopes  for  his 
own  use  ;  and,  during  his  life,  he  made  more  than  four 
hundred,  of  various  sizes  and  powers.  Under  the  pat- 
ronage of  George  the  Third,  he  completed,  in  1789,  his 
great  telescope,  having  a  tube  of  iron,  forty  feet  long, 
and  a  speculum,  forty-nine  and  a  half  inches  or  more 
than  four  feet  in  diameter.  Let  us  endeavor  to  form  a 
just  conception  of  this  gigantic  instrument,  which  we 
can  do  only  by  dwelling  on  its  dimensions,  and  compar- 
ing them  with  those  of  other  objects  with  which  we  are 
familiar,  as  the  length  or  height  of  a  house,  and  the 
breadth  of  a  hogshead  or  cistern,  of  known  dimensions. 
The  reflector  alone  weighed  nearly  a  ton.  So  large 
and  ponderous  an  instrument  must  require  a  vast  deal 
of  machinery  to  work  it,  and  to  keep  it  steady ;  and, 
accordingly,  the  frame-work  surrounding  it  was  formed 
of  heavy  timbers,  and  resembled  the  frame  of  a  large 
building.  When  one  of  the  largest  of  the  fixed  stars,  as 
Sirius,  is  entering  the  field  of  this  telescope,  its  approach 


TELESCOPE.  „  37 

is  announced  by  a  bright  dawn,  like  that  which  pre- 
cedes the  rising  sun  ;  and  when  the  star  itself  enters  the 
field,  the  light  is  insupportable  to  the  naked  eye.  The 
planets  are  expanded  into  brilliant  luminaries,  like  the 
moon ;  and  innumerable  multitudes  of  stars  are  scat- 
tered like  glittering  dust  over  the  celestial  vault. 

The  great  Dorpat  telescope  is  of  more  recent  con- 
struction. It  was  made  by  Fraunhofer,  a  German  op- 
tician of  the  greatest  eminence,  at  Munich,  in  Bavaria, 
and  takes  its  name  from  its  being  attached  to  the  ob- 
servatory at  Dorpat,  in  Russia.  It  is  of  much  smaller 
dimensions  than  the  great  telescope  of  Herschel.  Its 
object-glass  is  nine  and  a  half  inches  in  diameter,  and 
its  length,  fourteen  feet.  Although  the  price  of  this  in- 
strument was  nearly  five  thousand  dollars,  yet  it  is  said 
that  this  sum  barely  covered  the  actual  expenses.  It 
weighs  five  thousand  pounds,  and  yet  is  turned  with  the 
finger.  In  facility  of  management,  it  has  greatly  the 
advantage  of  Herschel's  telescope.  Moreover,  the  sky 
of  England  is  so  much  of  the  time  unfavorable  for  as- 
tronomical observation,  that  one  hundred  good  hours 
(or  those  in  which  the  higher  powers  can  be  used)  are 
all  that  can  be  obtained  in  a  whole  year.  On  this  ac- 
count, and  on  account  of  the  difficulty  of  shifting  the 
position  of  the  instrument,  Herschel  estimated  that  it 
would  take  about  six  hundred  years  to  obtain  with  it 
even  a  momentary  glimpse  of  every  part  of  the  heavens. 
This  remark  shows  that  such  great  telescopes  are  un- 
suited  to  the  common  purposes  of  astronomical  observa- 
tion. Indeed,  most  of  Herschel's  discoveries  were 
made  with  his  small  telescopes ;  and  although,  for  cer- 
tain rare  purposes,  powers  were  applied  which  magni- 
fied seven  thousand  times,  yet,  in  most  of  his  observa- 
tions, powers  magnifying  only  two  or  three  hundred 
times  were  employed.  The  highest  power  of  the  Dor- 
pat  telescope  is  only  seven  hundred,  and  yet  the  direc- 
tor of  this  instrument,  Professor  Struve,  is  of  the  opin- 
ion, that  it  is  nearly  or  quite  equal  in  quality,  all  things 
considered,  to  Herschel's  forty-feet  reflector. 

4  L.  A. 


38  LETTERS  ON  ASTRONOMY. 

It  is  not  generally  understood  in  what  way  greatness 
of  size  in  a  telescope  increases  its  powers  ;  and  it  con- 
veys but  an  imperfect  idea  of  the  excellence  of  a  tele- 
scope, to  tell  how  much  it  magnifies.  In  the  same  in- 
strument, an  increase  of  magnifying  power  is  always 
attended  with  a  diminution  of  the  light  and  of  the  field 
of  view.  Hence,  the  lower  powers  generally  afford  the 
most  agreeable  views,  because  they  give  the  clearest 
light,  and  take  in  the  largest  space.  The  several  cir- 
cumstances which  influence  the  qualities  of  a  telescope 
are,  illuminating  power,  distinctness,  field  of  view,  and 
magnifying  power.  Large  mirrors  and  large  object- 
glasses  are  superior  to  smaller  ones,  because  they  collect 
a  larger  beam  of  light,  and  transmit  it  to  the  eye.  Stars 
which  are  invisible  to  the  naked  eye  are  rendered  visi- 
ble by  the  telescope,  because  this  instrument  collects 
and  conveys  to  the  eye  a  large  beam  of  the  few  rays 
which  emanate  from  the  stars;  whereas  a  beam  of 
these  rays  of  only  the  diameter  of  the  pupil  of  the  eye, 
would  afford  too  little  light  for  distinct  vision.  In  this 
particular,  large  telescopes  have  great  advantages  over 
small  ones.  The  great  mirror  of  HerschePs  forty-feet 
reflector  collects  and  conveys  to  the  eye  a  beam  more 
than  four  feet  in  diameter.  The  Dorpat  telescope  also 
transmits  to  the  eye  a  beam  nine  and  one  half  inches 
in  diameter.  This  seems  small,  in  comparison  with  the 
reflector ;  but  much  less  of  the  light  is  lost  on  passing 
through  the  glass  than  is  absorbed  by  the  mirror,  and 
the  mirror  is  very  liable  to  be  clouded  or  tarnished ; 
so  that  there  is  not  so  great  a  difference  in  the  two  in- 
struments, in  regard  to  illuminating  power,  as  might  be 
supposed  from  the  difference  of  size. 

Distinctness  of  view  is  all-important  to  the  perform- 
ance of  an  instrument.  The  object  may  be  sufficiently 
bright,  yet,  if  the  image  is  distorted,  or  ill-defined,  the 
illumination  is  of  little  consequence.  This  property 
depends  mainly  on  the  skill  with  which  all  the  imper- 
fections of  figure  and  color  in  the  glass  or  mirror  are 
corrected,  and  can  exist  in  perfection  only  when  the 


TELESCOPE.  39 

image  is  rendered  completely  achromatic,  and  when  all 
the  rays  that  proceed  from  each  point  in  the  object  are 
collected  into  corresponding  points  of  the  image,  un- 
accompanied by  any  other  rays.  Distinctness  is  very 
much  affected  by  the  steadiness  of  the  instrument. 
Every  one  knows  how  indistinct  a  page  becomes,  when 
a  book  is  passed  rapidly  backwards  and  forwards  be- 
fore the  eyes,  and  how  difficult  it  is  to  read  in  a  car- 
riage in  rapid  motion  on  a  rough  road. 

Field  of  view  is  another  important  consideration. 
The  finest  instruments  exhibit  the  moon,  for  example, 
not  only  bright  and  distinct,  in  all  its  parts,  but  they 
take  in  the  whole  disk  at  once ;  whereas,  the  inferior 
instruments,  when  the  higher  powers,  especially,  are  ap- 
plied, permit  us  to  see  only  a  small  part  of  the  moon  at 
once. 

I  hope,  my  friend,  that,  when  you  have  perused  these 
Letters,  or  rather,  while  you  are  perusing  them,  you  will 
have  frequent  opportunities  of  looking  through  a  good 
telescope.  I  even  anticipate  that  you  will  acquire  such 
a  taste  for  viewing  the  heavenly  bodies  with  the  aid  of 
a  good  glass,  that  you  will  deem  a  telescope  a  most 
suitable  appendage  to  your  library,  and  as  certainly  not 
less  an  ornament  to  it  than  the  more  expensive  statues 
with  which  some  people  of  fortune  adorn  theirs.  I 
will  therefore,  before  concluding  this  letter,  offer  you 
a  few  directions  for  using  the  telescope. 

Some  states  of  weather,  even  when  the  sky  is  clear, 
are  far  more  favorable  for  astronomical  observation  than 
others.  After  sudden  changes  of  temperature  in  the 
atmosphere,  the  medium  is  usually  very  unsteady.  If 
the  sun  shines  out  warm  after  a  cloudy  season,  the 
ground  first  becomes  heated,  and  the  air  that  is  nearest 
to  it  is  expanded,  and  rises,  while  the  colder  air  de- 
scends, and  thus  ascending  and  descending  currents  of 
air,  mingling  together,  create  a  confused  and  wavy  me- 
dium. The  same  cause  operates  when  a  current  of  hot 
air  rises  from  a  chimney ;  and  hence  the  state  of  the 
atmosphere  in  cities  and  large  towns  is  very  unfavora- 


40  LETTERS  ON  ASTRONOMY. 

ble  to  the  astronomer,  on  this  account,  as  well  as  on 
account  of  the  smoky  condition  in  which  it  is  usually 
found.  After  a  long  season  of  dry  weather,  also,  the 
air  becomes  smoky,  and  unfit  for  observation.  Indeed, 
foggy,  misty,  or  smoky,  air  is  so  prevalent  in  some 
countries,  that  only  a  very  few  times  in  the  whole  year 
can  be  found,  which  are  entirely  suited  to  observation, 
especially  with  the  higher  powers  ;  for  we  must  recol- 
lect, that  these  inequalities  and  imperfections  are  mag- 
nified by  telescopes,  as  well  as  the  objects  themselves. 
Thus,  as  I  have  already  mentioned,  not  more  than  one 
hundred  good  hours  in  a  year  could  be  obtained  for 
observation  with  Herschel's  great  telescope.  By  good 
hours.  Herschel  means  that  the  sky  must  be  very  clear, 
the  moon  absent,  no  twilight,  no  haziness,  no  violent 
wind,  and  no  sudden  change  of  temperature.  As  a 
general  fact,  the  warmer  climates  enjoy  a  much  finer 
sky  for  the  astronomer  than  the  colder,  having  many 
more  clear  evenings,  a  short  twilight,  and  less  change 
of  temperature.  The  watery  vapor  of  the  atmosphere, 
also,  is  more  perfectly  dissolved  in  hot  than  in  cold  air, 
and  the  more  water  air  contains,  provided  it  is  in  a 
state  of  perfect  solution,  the  clearer  it  is. 

A  certain  preparation  of  the  observer  himself  is  also 
requisite  for  the  nicest  observations  with  the  telescope. 
He  must  be  free  from  all  agitation,  and  the  eye  must 
not  recently  have  been  exposed  to  a  strong  light,  which 
contracts  the  pupil  of  the  eye.  Indeed,  for  delicate 
observations,  the  observer  should  remain  for  some  time 
beforehand  in  a  dark  room,  to  let  the  pupil  of  the  eye 
dilate.  By  this  means,  it  will  be  enabled  to  admit  a 
larger  number  of  the  rays  of  light.  In  ascending  the 
stairs  of  an  observatory,  visiters  frequently  get  out  of 
breath,  and  having  perhaps  recently  emerged  from  a 
strongly-lighted  apartment,  the  eye  is  not  in  a  favor- 
able state  for  observation.  Under  these  disadvantages, 
they  take  a  hasty  look  into  the  telescope,  and  it  is  no 
wonder  that  disappointment  usually  follows. 

Want  of  steadiness  is  a  great  difficulty  attending  the 


TELESCOPE.  %  41 

use  of  the  highest  magnifiers ;  for  the  motions  of  the 
instrument  are  magnified  as  well  as  the  object.  Hence, 
in  the  structure  of  observatories,  the  greatest  pains  is 
requisite,  to  avoid  all  tremor,  and  to  give  to  the  instru- 
ments all  possible  steadiness  ;  and  the  same  care  is  to 
be  exercised  by  observers.  In  the  more  refined  obser- 
vations, only  one  or  two  persons  ought  to  be  near  the 
instrument. 

In  general,  low  powers  afford  better  views  of  the 
heavenly  bodies  than  very  high  magnifiers.  It  may  be 
thought  absurd,  to  recommend  the  use  of  low  powers, 
in  respect  to  large  instruments  especially,  since  it  is 
commonly  supposed  that  the  advantage  of  large  instru- 
ments is,  that  they  will  bear  high  magnifying  powers. 
But  this  is  not  their  only,  nor  even  their  principal,  ad- 
vantage. A  good  light  and  large  field  are  qualities,  for 
most  purposes,  more  important  than  great  magnifying 
power ;  and  it  must  be  borne  in  mind,  that,  as  we  in- 
crease the  magnifying  power  in  a  given  instrument,  we 
diminish  both  the  illumination  and  the  field  of  view. 
Still,  different  objects  require  different  magnifying  pow- 
ers ;  and  a  telescope  is  usually  furnished  with  several 
varieties  of  powers,  one  of  which  is  best  fitted  for  view- 
ing the  moon,  another  for  Jupiter,  and  a  still  higher 
power  for  Saturn.  Comets  require  only  the  lowest 
magnifiers  ;  for  here,  our  object  is  to  command  as  much 
light,  and  as  large  a  field,  as  possible,  while  it  avails 
little  to  increase  the  dimensions  of  the  object.  On  the 
other  hand,  for  certain  double  stars,  (stars  which  ap- 
pear single  to  the  naked  eye,  but  double  to  the  tele- 
scope,) we  require  very  high  magnifiers,  in  order  to 
separate  these  minute  objects  so  far  from  each  other, 
that  the  interval  can  be  distinctly  seen.  Whenever  we 
exhibit  celestial  objects  to  inexperienced  observers,  it 
is  useful  to  precede  the  view  with  good  drawings  of 
the  objects,  accompanied  by  an  explanation  of  what 
each  appearance,  exhibited  in  the  telescope,  indicates. 
The  novice  is  told,  that  mountains  and  valleys  can  be 
seen  in  the  moon  by  the  aid  of  the  telescope ;  but,  on 
4* 


42  LETTERS  ON  ASTRONOMY. 

looking,  he  sees  a -confused  mass  of  light  and  shade, 
and  nothing  which  looks  to  him  like  either  mountains 
or  valleys.  Had  his  attention  been  previously  directed 
to  a  plain  drawing  of  the  moon,  and  each  particular 
appearance  interpreted  to  him,  he  would  then  have 
looked  through  the  telescope  with  intelligence  and 
satisfaction. 


LETTER  V. 

OBSERVATORIES. 

"  We,  though  from  heaven  remote,  to  heaven  will  move, 
With  strength  of  mind,  and  tread  the  abyss  above ; 
And  penetrate,  with  an  interior  light, 
Those  upper  depths  which  Nature  hid  from  sight. 
Pleased  we  will  be,  to  walk  along  the  sphere 
Of  shining  stars,  and  travel  with  the  year." — Ovid . 

AN  observatory  is  a  structure  fitted  up  expressly  for 
astronomical  observations,  and  furnished  with  suitable 
instruments  for  that  purpose. 

The  two  most  celebrated  observatories,  hitherto  built, 
are  that  of  Tycho  Brahe,  and  that  of  Greenwich,  near 
London.  The  observatory  of  Tycho  Brahe,  Fig.  5, 
was  constructed  at  the  expense  of  the  King  of  Den- 
mark, in  a  style  of  royal  magnificence,  and  cost  no  less 
than  two  hundred  thousand  crowns.  It  was  situated 
on  the  island  of  Huenna,  at  the  entrance  of  the  Baltic, 
and  was  called  Uraniburg,  or  the  palace  of  the  skies. 

Before  I  give  you  an  account  of  Tycho's  observatory, 
I  will  recite  a  few  particulars  respecting  this  great  as- 
tronomer himself. 

Tycho  Brahe  was  of  Swedish  descent,  and  of  noble 
family ;  but  having  received  his  education  at  the  Uni- 
versity of  Copenhagen,  and  spent  a  large  part  of  his  life 
in  Denmark,  he  is  usually  considered  as  a  Dane,  and 
quoted  as  a  Danish  astronomer.  He  was  born  in  the 
year  1546.  When  he  was  about  fourteen  years  old, 
there  happened  a  great  eclipse  of  the  sun,  which  awak- 
ened in  him  a  high  interest,  especially  when  he  saw  how 


OBSERVATORIES. 


43 


Fig.  5. 


44  LETTERS  ON  ASTRONOMY. 

accurately  all  the  circumstances  of  it  answered  to  the 
prediction  with  which  he  had  been  before  made  ac- 
quainted. He  was  immediately  seized  with  an  irresisti- 
ble passion  to  acquire  a  knowledge  of  the  science  which 
could  so  successfully  lift  the  veil  of  futurity.  His  friends 
had  destined  him  for  the  profession  of  law,  and,  from 
the  superior  talents  of  which  he  gave  early  promise,  and 
with  the  advantage  of  powerful  family  connexions,  they 
had  marked  out  for  him  a  distinguished  career  in  pub- 
lic life.  They  therefore  endeavored  to  discourage  him 
from  pursuing  a  path  which  they  deemed  so  much  less 
glorious  than  that,  and  vainly  sought,  by  various  means, 
to  extinguish  the  zeal  for  astronomy  which  was  kindled 
in  his  youthful  bosom.  Despising  all  the  attractions 
of  a  court,  he  contracted  an  alliance  with  a  peasant  girl, 
and,  in  the  peaceful  retirement  of  domestic  life,  desired 
no  happier  lot  than  to  peruse  the  grand  volume  which 
the  nocturnal  heavens  displayed  to  his  enthusiastic  im- 
agination. He  soon  established  his  fame  as  one  of  the 
greatest  astronomers  of  the  age,  and  monarchs  did  hom- 
age to  his  genius.  The  King  of  Denmark  became  his 
munificent  patron,  and  James  the  First,  King  of  Eng- 
land, when  he  went  to  Denmark  to  complete  his  mar- 
riage with  a  Danish  Princess,  passed  eight  days  with 
Tycho  in  his  observatory,  and,  at  his  departure,  ad- 
dressed to  the  astronomer  a  Latin  ode,  accompanied 
with  a  magnificent  present.  He  gave  him  also  his  royal 
license  to  print  his  works  in  England,  and  added  to  it 
the  following  complimentary  letter :  "  Nor  am  I  ac- 
quainted with  these  things  on  the  relation  of  others,  or 
from  a  mere  perusal  of  your  works,  but  I  have  seen 
them  with  my  own  eyes,  and  heard  them  with  my  own 
ears,  in  your  residence  at  Uraniburg,  during  the  various 
learned  and  agreeable  conversations  which  I  there  held 
with  you,  which  even  now  affect  my  mind  to  such  a 
degree,  that  it  is  difficult  to  decide,  whether  I  recollect 
them  with  greater  pleasure  or  admiration."  Admiring 
disciples  also  crowded  to  this  sanctuary  of  the  sciences, 
to  acquire  a  knowledge  of  the  heavens. 


OBSERVATORIES.  %  45 

The  observatory  consisted  of  a  main  building,  which 
was  square,  each  side  being  sixty  feet,  and  of  large 
wings  in  the  form  of  round  towers.  The  whole  was 
executed  in  a  style  of  great  magnificence,  and  Tycho, 
who  was  a  nobleman  by  descent,  gratified  his  taste  for 
splendor  and  ornament,  by  giving  to  every  part  of  the 
structure  an  air  of  the  most  finished  elegance.  Nor 
were  the  instruments  with  which  it  was  furnished  less 
magnificent  than  the  buildings.  They  were  vastly 
larger  than  had  before  been  employed  in  the  survey  of 
the  heavens,  and  many  of  them  were  adorned  with 
costly  ornaments.  The  cut  on  page  46,  Fig.  6,  repre- 
sents one  of  Tycho's  large  and  splendid  instruments, 
(an  astronomical  quadrant,)  on  one  side  of  which  was 
figured  a  representation  of  the  astronomer  and  his  as- 
sistants, in  the  midst  of  their  instruments,  and  intently 
engaged  in  making  and  recording  observations.  It  con- 
veys to  us  a  striking  idea  of  the  magnificence  of  his  ar- 
rangements, and  of  the  extent  of  his  operations. 

Here  Tycho  sat  in  state,  clad  in  the  robes  of  nobili- 
ty, and  supported  throughout  his  establishment  the  eti- 
quette due  to  his  rank.  His  observations  were  more 
numerous  than  all  that  had  ever  been  made  before,  and 
they  were  carried  to  a  degree  of  accuracy  that  is  aston- 
ishing, when  we  consider  that  they  were  made  without 
the  use  of  the  telescope,  which  was  not  yet  invented. 

Tycho  carried  on  his  observations  at  Uraniburg  for 
about  twenty  years,  during  which  time  he  accumulated 
an  immense  store  of  accurate  and  valuable  facts,  which 
afforded  the  groundwork  of  the  discovery  of  the  great 
laws  of  the  solar  system  established  by  Kepler,  of  whom 
I  shall  tell  you  more  hereafter. 

But  the  high  marks  of  distinction  which  Tycho  en- 
joyed, not  only  from  his  own  Sovereign,  but  also  from 
foreign  potentates,  provoked  the  envy  of  the  courtiers 
of  his  royal  patron.  They  did  not  indeed  venture  to 
make  their  attacks  upon  him  while  his  generous  patron 
was  living ;  but  the  King  was  no  sooner  dead,  and  suc- 
ceeded by  a  young  monarch,  who  did  not  feel  the  same 


46 


LETTERS  ON  ASTRONOMY. 


Pig.  6. 


OBSERVATORIES.  47 

interest  in  protecting  and  encouraging  this  great  orna- 
ment of  the  kingdom,  than  his  envious  foes  carried  into 
execution  their  long-meditated  plot  for  his  ruin.  They 
represented  to  the  young  King,  that  the  treasury  was 
exhausted,  and  that  it  was  necessary  to  retrench  a  num- 
ber of  pensions,  which  had  been  granted  for  useless 
purposes,  and  in  particular  that  of  Tycho,  which,  they 
maintained,  ought  to  be  conferred  upon  some  person 
capable  of  rendering  greater  services  to  the  state.  By 
these  means,  they  succeeded  in  depriving  him  of  his 
support,  and  he  was  compelled  to  retreat  under  the 
hospitable  mansion  of  a  friend  in  Germany.  Here  he 
became  known  to  the  Emperor,  who  invited  him  to 
Prague,  where,  with  an  ample  stipend,  he  resumed  his 
labors.  But,  though  surrounded  with  affectionate  friends 
and  admiring  disciples,  he  was  still  an  exile  in  a  foreign 
land.  Although  his  country  had  been  base  in  its  in- 
gratitude, it  was  yet  the  land  which  he  loved  ;  the 
scene  of  his  earliest  affection ;  the  theatre  of  his  scien- 
tific glory.  These  feelings  continually  preyed  upon  his 
mind,  and  his  unsettled  spirit  was  ever  hovering  among 
his  native  mountains.  In  this  condition  he  was  at- 
tacked by  a  disease  of  the  most  painful  kind,  and, 
though  its  agonizing  paroxysms  had  lengthened  inter- 
missions, yet  he  saw  that  death  was  approaching.  He 
implored  his  pupils  to  persevere  in  their  scientific  la- 
bors ;  he  conversed  with  Kepler  on  some  of  the  pro- 
foundest  points  of  astronomy ;  and  with  these  secular 
occupations  he  mingled  frequent  acts  of  piety  and  de- 
votion. In  this  happy  condition  he  expired,  without 
pain,  at  the  age  of  fifty-five.* 

The  observatory  at  Greenwich  was  not  built  until  a 
hundred  years  after  that  of  Tycho  Brahe,  namely,  in 
1676.  The  great  interests  of  the  British  nation,  which 
are  involved  in  navigation,  constituted  the  ruling  motive 
with  the  government  to  lend  their  aid  in  erecting  and 
maintaining  this  observatory. 

*  Brewster's  Life  of  Newton. 


48  LETTERS  ON  ASTRONOMY. 

The  site  of  the  observatory  at  Greenwich  is  on  a 
commanding  eminence  facing  the  River  Thames,  five 
miles  east  of  the  central  parts  of  London.  Being  part 
of  a  royal  park,  the  neighboring  grounds  are  in  no  dan- 
ger of  being  occupied  by  buildings,  so  as  to  obstruct  the 
view.  It  is  also  in  full  view  of  the  shipping  on  the 
Thames  ;  and,  according  to  a  standing  regulation  of  the 
observatory,  at  the  instant  of  one  o'clock,  every  day,  a 
huge  ball  is  dropped  from  over  the  house,  as  a  signal 
to  the  commanders  of  vessels  for  regulating  their  chro- 
nometers. 

The  buildings  comprise  a  series  of  rooms,  of  sufficient 
number  and  extent  to  accommodate  the  different  instru- 
ments, the  inmates  of  the  establishment,  and  the  libra- 
ry ;  and  on  the  top  is  a  celebrated  camera  obscura,  ex- 
hibiting a  most  distinct  and  perfect  picture  of  the  grand 
and  unrivalled  scenery  which  this  eminence  commands. 

This  establishment,  by  the  accuracy  and  extent  of 
its  observations,  has  contributed  more  than  all  other  in- 
stitutions to  perfect  the  science  of  astronomy. 

To  preside  over  and  direct  this  great  institution,  a 
man  of  the  highest  eminence  in  the  science  is  appoint- 
ed by  the  government,  with  the  title  of  Astronomer 
Royal.  He  is  paid  an  ample  salary,  with  the  under- 
standing that  he  is  to  devote  himself  exclusively  to  the 
business  of  the  observatory.  The  astronomers  royal  of 
the  Greenwich  observatory,  from  the  time  of  its  first 
establishment,  in  1676,  to  the  present  time,  have  con- 
stituted a  series  of  the  proudest  names  of  which  Brit- 
ish science  can  boast.  A  more  detailed  sketch  of  their 
interesting  history  will  be  given  towards  the  close  of 
these  Letters. 

Six  assistants,  besides  inferior  laborers,  are  constant- 
ly in  attendance ;  and  the  business  of  making  and  re- 
cording observations  is  conducted  with  the  utmost  sys- 
tem and  order. 

The  great  objects  to  be  attained  in  the  construction 
of  an  observatory  are,  a  commanding  and  unobstructed 
view  of  the  heavens ;  freedom  from  causes  that  affect 


OBSERVATORIES.  *  49 

the  transparency  and  uniform  state  of  the  atmosphere, 
such  as  fires,  smoke,  or  marshy  grounds ;  mechanical 
facilities  for  the  management  of  instruments,  and,  es- 
pecially, every  precaution  that  is  necessary  to  secure 
perfect  steadiness.  This  last  consideration  is  one  of  the 
greatest  importance,  particularly  in  the  use  of  very  large 
magnifiers ;  for  we  must  recollect,  that  any  motion  in 
the  instrument  is  magnified  by  the  full  power  of  the 
glass,  and  gives  a  proportional  unsteadiness  to  the  ob- 
ject. A  situation  is  therefore  selected  as  remote  as  pos- 
sible from  public  roads,  (for  even  the  passing  of  carriages 
would  give  a  tremulous  motion  to  the  ground,  which 
would  be  sensible  in  large  instruments,)  and  structures 
of  solid  masonry  are  commenced  deep  enough  in  the 
ground  to  be  unaffected  by  frost,  and  built  up  to  the 
height  required,  without  any  connexion  with  the  other 
parts  of  the  building.  Many  observatories  are  furnish- 
ed with  a  movable  dome  for  a  roof,  capable  of  revolving 
on  rollers,  so  that  instruments  penetrating  through  the 
roof  may  be  easily  brought  to  bear  upon  any  point  at 
or  near  the  zenith. 

You  will  not  perhaps  desire  me  to  go  into  a  minute 
description  of  all  the  various  instruments  that  are  used 
in  a  well-constructed  observatory.  Nor  is  this  neces- 
sary, since  a  very  large  proportion  of  all  astronomical 
observations  are  taken  on  the  meridian,  by  means  of  the 
transit  instrument  and  clock.  When  a  body,  in  its  di- 
urnal revolution,  comes  to  the  meridian,  it  is  at  its  high- 
est point  above  the  horizon,  and  is  then  least  affected 
by  refraction  and  parallax.  This,  then,  is  the  most  fa- 
vorable position  for  taking  observations  upon  it.  More- 
over, it  is  peculiarly  easy  to  take  observations  on  a  body 
when  in  this  situation.  Hence  the  transit  instrument 
and  clock  are  the  most  important  members  of  an  astro- 
nomical observatory.  You  will,  therefore,  expect  me 
to  give  you  some  account  of  these  instruments. 

The  transit  instrument  is  a  telescope  which  is  fixed 
permanently  in  the  meridian,  and  moves  only  in  that 
plane.  The  accompanying  diagram,  Fig.  7,  represents 

5  L.  A. 


50  LETTERS  ON  ASTRONOMY. 

a  side  view  of  a  portable  transit  instrument,  exhibiting 
the  telescope  supported  on  a  firm  horizontal  axis,  on 
which  it  turns  in  the  plane  of  the  meridian,  from  the 
south  point  of  the  horizon  through  the  zenith  to  the 
north  point.  It  can  therefore  be  so  directed  as  to  ob- 
serve the  passage  of  a  star  across  the  meridian  at  any 
altitude.  The  accompanying  graduated  circle  enables 


Fig.  7. 


the  observer  to  set  the  instrument  at  any  required  alti- 
tude, corresponding  to  the  known  altitude  at  which  the 
body  to  be  observed  crosses  the  meridian.  Or  it  may 
be  used  to  measure  the  altitude  of  a  body,  or  its  zenith 
distance,  at  the  time  of  its  meridian  passage.  Near  the 
circle  may  be  seen  a  spirit-level,  which  serves  to  show 
when  the  axis  is  exactly  on  a  level  with  the  horizon. 
The  framework  is  made  of  solid  metal,  (usually  brass,) 
every  thing  being  arranged  with  reference  to  keeping 
the  instrument  perfectly  steady.  It  stands  on  screws, 
which  not  only  afford  a  steady  support,  but  are  useful 


OBSERVATORIES.  *  51 

for  adjusting  the  instrument  to  a  perfect  level.  The 
transit  instrument  is  sometimes  fixed  immovably  to  a 
solid  foundation,  as  a  pillar  of  stone,  which  is  built  up 
from  a  depth  in  the  ground  below  the  reach  of  frost. 
When  enclosed  in  a  building,  as  in  an  observatory,  the 
stone  pillar  is  carried  up  separate  from  the  walls  and 
floors  of  the  building,  so  as  to  be  entirely  free  from 
the  agitations  to  which  they  are  liable. 

The  use  of  the  transit  instrument  is  to  show  the 
precise  instant  when  a  heavenly  body  is  on  the  me- 
ridian, or  to  measure  the  time  it  occupies  in  crossing 
the  meridian.  The  astronomical  clock  is  the  constant 
companion  of  the  transit  instrument.  This  clock  is  so 
regulated  as  to  keep  exact  pace  with  the  stars,  and  of 
course  with  the  revolution  of  the  earth  on  its  axis  ;  that 
is,  i^  is  regulated  to  sidereal  time.  It  measures  the 
progress  of  a  star,  indicating  an  hour  for  every  fifteen 
degrees,  and  twenty-four  hours  for  the  whole  period  of 
the  revolution  of  the  star.  Sidereal  time  commences 
when  the  vernal  equinox  is  on  the  meridian,  just  as 
solar  time  commences  when  the  sun  is  on  the  meridian. 
Hence  the  hour  by  the  sidereal  clock  has  no  correspon- 
dence with  the  hour  of  the  day,  but  simply  indicates  how 
long  it  is  since  the  equinoctial  point  crossed  the  merid- 
ian. For  example,  the  clock  of  an  observatory  points 
to  three  hours  and  twenty  minutes ;  this  may  be  in  the 
morning,  at  noon,  or  any  other  time  of  the  day, — for  it 
merely  shows  that  it  is  three  hours  and  twenty  minutes 
since  the  equinox  was  on  the  meridian.  Hence,  when  a 
star  is  on  the  meridian,  the  clock  itself  shows  its  right 
ascension,  which  you  will  recollect  is  the  angular  dis- 
tance measured  on  the  equinoctial,  from  the  point  of 
intersection  of  the  ecliptic  and  equinoctial,  called  the 
vernal  equinox,  reckoning  fifteen  degrees  for  every  hour, 
and  a  proportional  number  of  degrees  and  minutes  for  a 
less  period.  I  have  before  remarked,  that  a  very  large 
portion  of  all  astronomical  observations  are  taken  when 
the  bodies  are  on  the  meridian,  by  means  of  the  transit 
instrument  and  clock. 


52  LETTERS  ON  ASTRONOMY. 

Having  now  described  these  instruments,  I  will  next 
explain  the  manner  of  using  them  for  different  obser- 
vations. Any  thing  becomes  a  measure  of  time,  which 
divides  duration  equally.  The  equinoctial,  therefore,  is 
peculiarly  adapted  to  this  purpose,  since,  in  the  daily 
revolution  of  the  heavens,  equal  portions  of  the  equi- 
noctial pass  under  the  meridian  in  equal  times.  The 
only  difficulty  is,  to  ascertain  the  amount  of  these  por- 
tions for  given  intervals.  Now,  the  clock  shows  us 
exactly  this  amount;  for,  when  regulated  to  sidereal 
time,  (as  it  easily  may  be,)  the  hour-hand  keeps  ex- 
act pace  with  the  equator,  revolving  once  on  the  dial- 
plate  of  the  clock  while  the  equator  turns  once  by  the 
revolution  of  the  earth.  The  same  is  true,  also,  of  all 
the  small  circles  of  diurnal  revolution ;  they  all  turn 
exactly  at  the  same  rate  as  the  equinoctial,  and  a  star 
situated  any  where  between  the  equator  and  the  pole 
will  move  in  its  diurnal  circle  along  with  the  clock,  in 
the  same  manner  as  though  it  were  in  the  equinoctial. 
Hence,  if  we  note  the  interval  of  time  between  the  pas- 
sage of  any  two  stars,  as  shown  by  the  clock,  we  have 
a  measure  of  the  number  of  degrees  by  which  they  are 
distant  from  each  other  in  right  ascension.  Hence  we 
see  how  easy  it  is  to  take  arcs  of  right  ascension :  the 
transit  instrument  shows  us  when  a  body  is  on  the  me- 
ridian ;  the  clock  indicates  how  long  it  is  since  the 
vernal  equinox  passed  it,  which  is  the  right  ascension 
itself;  or  it  tells  us  the  difference  of  right  ascension 
between  any  two  bodies,  simply  by  indicating  the  differ- 
ence in  time  between  their  periods  of  passing  the  merid- 
ian. Again,  it  is  easy  to  take  the  declination  of  a  body 
when  on  the  meridian.  By  declination,  you  will  recol- 
lect, is  meant  the  distance  of  a  heavenly  body  from  the 
equinoctial ;  the  same,  indeed,  as  latitude  on  the  earth. 
When  a  star  is  passing  the  meridian,  if,  on  the  instant 
of  crossing  the  meridian  wire  of  the  telescope,  we  take 
its  distance  from  the  north  pole,  (which  may  readily  be 
done,  because  the  position  of  the  pole  is  always  known, 
being  equal  to  the  latitude  of  the  place,)  and  subtract 


OBSERVATORIES.  »  53 

this  distance  from  ninety  degrees,  the  remainder  will  be 
the  distance  from  the  equator,  which  is  the  declination. 
You  will  ask,  why  we  take  this  indirect  method  of  find- 
ing the  declination  ?  Why  we  do  not  rather  take  the 
distance  of  the  star  from  the  equinoctial,  at  once  ?  I 
answer,  that  it  is  easy  to  point  an  instrument  to  the 
north  pole,  and  to  ascertain  its  exact  position,  and  of 
course  to  measure  any  distance  from  it  on  the  meridian, 
while,  as  there  is  nothing  to  mark  the  exact  situation 
of  the  equinoctial,  it  is  not  so  easy  to  take  direct  meas- 
urements from  it.  When  we  have  thus  determined 
the  situation  of  a  heavenly  body,  with  respect  to  two 
great  circles  at  right  angles  with  each  other,  as  in  the 
present  case,  the  distance  of  a  body  from  the  equator 
and  from  the  equinoctial  colure,  or  that  meridian  which 
passes  though  the  vernal  equinox,  we  know  its  relative 
position  in  the  heavens  ;  and  when  we  have  thus  de- 
termined the  relative  positions  of  all  the  stars,  we  may 
lay  them  down  on  a  map  or  a  globe,  exactly  as  we  do 
places  on  the  earth,  by  means  of  their  latitude  and  lon- 
gitude. 

The  foregoing  is  only  a  specimen  of  the  various  uses 
of  the  transit  instrument,  in  finding  the  relative  places 
of  the  heavenly  bodies.  Another  use  of  this  excellent 
instrument  is,  to  regulate  our  clocks  and  watches.  By 
an  observation  with  the  transit  instrument,  we  find 
when  the  sun's  centre  is  on  the  meridian.  This  is  the 
exact  time  of  apparent  noon.  But  watches  and  clocks 
usually  keep  mean  time,  and  therefore,  in  order  to  set 
our  timepiece  by  the  transit  instrument,  we  must  apply 
to  the  apparent  time  of  noon  the  equation  of  time,  as 
will  be  explained  in  my  next  Letter. 

A  noon-mark  may  easily  be  made  by  the  aid  of  the 
transit  instrument.  A  window  sill  is  frequently  selected 
as  a  suitable  place  for  the  mark,  advantage  being  taken 
of  the  shadow  projected  upon  it  by  the  perpendicular 
casing  of  the  window.  Let  an  assistant  stand,  with  a 
rule  laid  on  the  line  of  shadow,  and  with  a  knife  ready 
to  make  the  mark,  the  instant  when  the  observer  at  the 
5* 


54  LETTERS  ON  ASTRONOMY. 

transit  instrument  announces  that  the  centre  of  the  sun 
is  on  the  meridian.  By  a  concerted  signal,  as  the 
stroke  of  a  bell,  the  inhabitants  of  a  town  may  all  fix 
a  noon-mark  from  the  same  observation.  If  the  signal 
be  given  on  one  of  the  days  when  apparent  time  and 
mean  time  become  equal  to  each  other,  as  on  the  twen- 
ty-fourth of  December,  no  equation  of  time  is  required. 

As  a  noon-mark  is  convenient  for  regulating  time- 
pieces, I  will  point  out  a  method  of  making  one,  which 
may  be  practised  without  the  aid  of  the  telescope. 
Upon  a  smooth,  level  plane,  freely  exposed  to  the  sun, 
with  a  pair  of  compasses  describe  a  circle.  In  the  cen- 
tre, where  the  leg  of  the  compasses  stood,  erect  a  per- 
pendicular wire  of  such  a  length,  that  the  termination 
of  its  shadow  shall  fall  upon  the  circumference  of  the 
circle  at  some  hour  before  noon,  as  about  ten  o'clock. 
Make  a  small  dot  at  the  point  where  the  end  of  the 
shadow  falls  upon  the  circle,  and  do  the  same  where  it 
falls  upon  it  again  in  the  afternoon.  Take  a  point  half- 
way between  these  two  points,  and  from  it  draw  a  line 
to  the  centre,  and  it  will  be  a  true  meridian  line.  The 
direction  of  this  line  would  be  the  same,  whether  it 
were  made  in  the  Summer  or  in  the  Winter  ;  but  it  is 
expedient  to  draw  it  about  the  fifteenth  of  June,  for  then 
the  shadow  alters  its  length  most  rapidly,  and  the  mo- 
ment of  its  crossing  the  wire  will  be  more  definite, 
than  in  the  Winter.  At  this  time  of  year,  also,  the  sun 
and  clock  agree,  or  are  together,  as  will  be  more  fully  ex- 
plained in  my  next  Letter ;  whereas,  at  other  times  of 
the  year,  the  time  of  noon,  as  indicated  by  a  common 
clock,  would  not  agree  with  that  indicated  by  the  sun. 
If  the  upper  end  of  the  wire  is  flattened,  and  a  small 
hole  is  made  in  it,  through  which  the  sun  may  shine, 
the  instant  when  this  bright  spot  falls  upon  the  circle 
will  be  better  defined  than  the  termination  of  the  shadow. 

Another  important  instrument  of  the  observatory  is 
the  mural  circle.  It  is  a  graduated  circle,  usually  of 
very  large  size,  fixed  permanently  in  the  plane  of  the 
meridian,  and  attached  firmly  to  a  perpendicular  wall ; 


OBSERVATORIES.  »  55 

and  on  its  centre  is  a  telescope,  which  revolves  along 
with  it,  and  is  easily  brought  to  bear  on  any  object  in 
any  point  in  the  meridian.  It  is  made  of  large  size, 
sometimes  twenty  feet  in  diameter,  in  order  that  very 
small  angles  may  be  measured  on  its  limb  ;  for  it  is  ob- 
vious that  a  small  angle,  as  one  second,  will  be  a  larger 
space  on  the  limb  of  an  instrument,  in  proportion  as 
the  instrument  itself  is  larger.  The  vertical  circle  usu- 
ally connected  with  the  transit  instrument,  as  in  Fig.  7, 
may  indeed  be  employed  for  the  same  purposes  as  the 
mural  circle,  namely,  to  measure  arcs  of  the  meridian, 
as  meridian  altitudes,  zenith  distances,  north  polar  dis- 
tances, and  declinations ;  but  as  that  circle  must  nec- 
essarily be  small,  and  therefore  incapable  of  measuring 
very  minute  angles,  the  mural  circle  is  particularly  use- 
ful in  measuring  these  important  arcs.  It  is  very  diffi- 
cult to  keep  so  large  an  instrument  perfectly  steady ; 
and  therefore  it  is  attached  to  a  massive  wall  of  solid 
masonry,  and  is  hence  called  a  mural  circle,  from  a 
Latin  word,  (murus,)  which  signifies  a  wall. 

The  diagram,  Fig.  8,  page  56,  represents  a  mural 
circle  fixed  to  its  wall,  and  ready  for  observations.  It 
will  be  seen,  that  every  expedient  is  employed  to  give 
the  instrument  firmness  of  parts  and  steadiness  of  posi- 
tion. The  circle  is  of  solid  metal,  usually  of  brass,  and 
it  is  strengthened  by  numerous  radii,  which  keep  it  from 
warping  or  bending ;  and  these  are  made  in  the  form 
of  hollow  cones,  because  that  is  the  figure  which  unites 
in  the  highest  degree  lightness  and  strength.  On  the 
rim  of  the  instrument,  at  A,  you  may  observe  a  micro- 
scope. This  is  attached  to  a  micrometer, — a  delicate 
piece  of  apparatus,  used  for  reading  the  minute  subdi- 
visions of  angles ;  for,  after  dividing  the  limb  of  the 
instrument  as  minutely  as  possible,  it  will  then  be  nec- 
essary to  magnify  those  divisions  with  the  microscope, 
and  subdivide  each  of  these  parts  with  the  micrometer. 
Thus,  if  we  have  a  mural  circle  twenty  feet  in  diame- 
ter, and  of  course  nearly  sixty-three  feet  in  circumfer- 
ence, since  there  are  twenty-one  thousand  and  six  hun- 


56  LETTERS  ON  ASTRONOMY. 

dred  minutes  in  the  whole  circle,  we  shall  find,  by  cal- 
culation, that  one  minute  would  occupy,  on  the  limb  of 
such  an  instrument,  only  about  one  thirtieth  of  an  inch, 
and  a  second,  only  one  eighteen  hundredth  of  an  inch. 
We  could  not,  therefore,  hope  to  carry  the  actual  di- 
visions to  a  greater  degree  of  minuteness  than  minutes ; 
but  each  of  these  spaces  may  again  be  subdivided  into 
seconds  by  the  micrometer. 

Fig.  8. 


From  these  statements,  you  will  acquire  some  faint 
idea  of  the  extreme  difficulty  of  making  perfect  astro- 
nomical instruments,  especially  where  they  are  intended 
to  measure  such  minute  angles  as  one  second.  Indeed, 
the  art  of  constructing  astronomical  instruments  is  one 
which  requires  such  refined  mechanical  genius, — so  su- 


OBSERVATORIES.  %  57 

perior  a  mind  to  devise,  and  so  delicate  a  hand  to  ex- 
ecute,— that  the  most  celebrated  instrument-makers 
take  rank  with  the  most  distinguished  astronomers ; 
supplying,  as  they  do,  the  means  by  which  only  the 
latter  are  enabled  to  make  these  great  discoveries.  As- 
tronomers have  sometimes  made  their  own  telescopes ; 
but  they  have  seldom,  if  ever,  possessed  the  refined 
manual  skill  which  is  requisite  for  graduating  delicate 
instruments. 

The  sextant  is  also  one  of  the  most  valuable  instru- 
ments for  taking  celestial  arcs,  or  the  distance  between 
any  two  points  on  the  celestial  sphere,  being  applicable 
to  a  much  greater  number  of  purposes  than  the  instru- 
ments already  described.  It  is  particularly  valuable  for 
measuring  celestial  arcs  at  sea,  because  it  is  not,  like 
most  astronomical  instruments,  affected  by  the  motion 
of  the  ship.  The  principle  of  the  sextant  may  be  briefly 
described,  as  follows :  it  gives  the  angular  distance  be- 
tween any  two  bodies  on  the  celestial  sphere,  by  reflect- 
ing the  image  of  one  of  the  bodies  so  as  to  coincide 
with  the  other  body,  as  seen  directly.  The  arc  through 
which  the  reflector  is  turned,  to  bring  the  reflected  body 
to  coincide  with  the  other  body,  becomes  a  measure  of 
the  angular  distance  between  them.  By  keeping  this 
principle  in  view,  you  will  be  able  to  understand  the 
use  of  the  several  parts  of  the  instrument,  as  they  are 
exhibited  in  the  diagram,  Fig.  9,  page  58. 

It  is,  you  observe,  of  a  triangular  shape,  and  it  is 
made  strong  and  firm  by  metallic  cross-bars.  It  has  two 
reflectors,  I  and  H,  called,  respectively,  the  index  glass 
and  the  horizon  glass,  both  of  which  are  firmly  fixed 
perpendicular  to  the  plane  of  the  instrument.  The 
index  glass  is  attached  to  the  movable  arm,  I  D,  and 
turns  as  this  is  moved  along  the  graduated  limb,  E  F. 
This  arm  also  carries  a  vernier,  at  D,  a  contrivance 
which,  like  the  micrometer,  enables  us  to  take  off  mi- 
nute parts  of  the  spaces  into  which  the  limb  is  divided. 
The  horizon  glass,  H,  consists  of  two  parts ;  the  upper 
part  being  transparent  or  open,  so  that  the  eye,  looking 


58 


LETTERS  ON  ASTRONOMY. 


Fig.  9. 


through  the  telescope,  T,  can  see  through  it  a  distant 
body,  as  a  star  at  S,  while  the  lower  part  is  a  reflector. 
Suppose  it  were  required  to  measure  the  angular  dis- 
tance between  the  moon  and  a  certain  star, — the  rnoon 
being  at  M,  and  the  star  at  S.  The  instrument  is  held 
firmly  in  the  hand,  so  that  the  eye,  looking  through  the 
telescope,  sees  the  star,  S,  through  the  transparent  part 
of  the  horizon  glass.  Then  the  movable  arm,  I D,  is 
moved  from  F  towards  E,  until  the  image  of  M  is  re- 
flected down  to  S,  when  the  number  of  degrees  and 
parts  of  a  degree  reckoned  on  the  limb,  from  F  to  the 
index  at  D,  will  show  the  angular  distance  between  the 
two  bodies. 


TIME  AND  THE   CALENDAR.  59 


LETTER  VI. 

TIME  AND  THE  CALENDAR. 

"  From  old  Eternity's  mysterious  orb 
Was  Time  cut  off,  and  cast  beneath  the  skies."— Young. 

HAVING  hitherto  been  conversant  only  with  the  many 
fine  and  sentimental  things  which  the  poets  have  sung 
respecting  Old  Time,  perhaps  you  will  find  some  diffi- 
culty in  bringing  down  your  mind  to  the  calmer  con- 
sideration of  what  time  really  is,  and  according  to  what 
different  standards  it  is  measured  for  different  purposes. 
You  will  not,  however,  I  think,  find  the  subject  even 
in  our  matter-of-fact  and  unpoetical  way  of  treating  it, 
altogether  uninteresting.  What,  then,  is  time?  Time 
is  a  measured  portion  of  indefinite  duration.  It  con- 
sists of  equal  portions  cut  off  from  eternity,  as  a  line  on 
the  surface  of  the  earth  is  separated  from  its  contiguous 
portions  that  constitute  a  great  circle  of  the  sphere,  by 
applying  to  it  a  two-foot  scale ;  or  as  a  few  yards  of 
cloth  are  measured  off  from  a  piece  of  unknown  or  in- 
definite extent. 

Any  thing,  or  any  event  which  takes  place  at  equal 
intervals,  may  become  a  measure  of  time.  Thus,  the 
pulsations  of  the  wrist,  the  flowing  of  a  given  quantity 
of  sand  from  one  vessel  to  another,  as  in  the  hourglass, 
the  beating  of  a  pendulum,  and  the  revolution  of  a  star, 
have  been  severally  employed  as  measures  of  time.  But 
the  great  standard  of  time  is  the  period  of  the  revolu- 
tion of  the  earth  on  its  axis,  which,  by  the  most  exact 
observations,  is  found  to  be  always  the  same.  I  have 
anticipated  a  little  of  this  subject,  in  giving  an  account 
of  the  transit  instrument  and  clock,  but  I  propose,  in 
this  letter,  to  enter  into  it  more  at  large. 

The  time  of  the  earth's  revolution  on  its  axis,  as  al- 
ready explained,  is  called  a  sidereal  day,  and  is  deter- 
mined by  the  revolution  of  a  star  in  the  heavens.  This 


60  LETTERS  ON  ASTRONOMY. 

interval  is  divided  into  twenty-four  sidereal  hours.  Ob- 
servations taken  on  numerous  stars,  in  different  ages 
of  the  world,  show  that  they  all  perform  their  diurnal 
revolution  in  the  same  time,  and  that  their  motion,  dur- 
ing any  part  of  the  revolution,  is  always  uniform.  Here, 
then,  we  have  an  exact  measure  of  time,  probably  more 
exact  than  any  thing  which  can  be  devised  by  art. 
Solar  time  is  reckoned  by  the  apparent  revolution  of 
the  sun  from  the  meridian  round  to  the  meridian  again. 
Were  the  sun  stationary  in  the  heavens,  like  a  fixed 
star,  the  time  of  its  apparent  revolution  would  be  equal 
to  the  revolution  of  the  earth  on  its  axis,  and  the  solar 
and  the  sidereal  days  would  be  equal.  But,  since  the 
sun  passes  from  west  to  east,  through  three  hundred  and 
sixty  degrees,  in  three  hundred  and  sixty-five  and  one 
fourth  days,  it  moves  eastward  nearly  one  degree  a  day. 
While,  therefore,  the  earth  is  turning  round  on  its  axis, 
the  sun  is  moving  in  the  same  direction,  so  that,  when 
we  have  come  round  under  the  same  celestial  meridian 
from  which  we  started,  we  do  not  find  the  sun  there, 
but  he  has  moved  eastward  nearly  a  degree,  and  the 
earth  must  perform  so  much  more  than  one  complete 
revolution,  before  we  come  under  the  sun  again.  Now, 
since  we  move,  in  the  diurnal  revolution,  fifteen  de- 
grees in  sixty  minutes,  we  must  pass  over  one  degree 
in  four  minutes.  It  takes,  therefore,  four  minutes  for 
us  to  catch  up  with  the  sun,  after  we  have  made  one 
complete  revolution.  Hence  the  solar  day  is  about  four 
minutes  longer  than  the  sidereal ;  and  if  we  were  to  reck- 
on the  sidereal  day  twenty-four  hours,  we  should  reckon 
the  solar  day  twenty-four  hours  four  minutes.  To  suit 
the  purposes  of  society  at  large,  however,  it  is  found  more 
convenient  to  reckon  the  solar  days  twenty-four  hours, 
and  throw  the  fraction  into  the  sidereal  day.  Then, 

24h.  4m.  :  24h.  :  :  24h.  :  23h.  56m.  4s. 
That  is,  when  we  reduce  twenty-four  hours  and  four 
minutes  to  twenty-four  hours,  the  same  proportion  will 
require  that  we  reduce  the  sidereal  day  from  twenty-four 
hours  to  twenty-three  hours  fifty-six  minutes  four  sec- 


TIME  AND  THE  CALENDAR.,  61 

onds  ;  or,  in  other  words,  a  sidereal  day  is  such  a  part 
of  a  solar  day.  The  solar  days,  however,  do  not  always 
differ  from  the  sidereal  by  precisely  the  same  fraction, 
since  they  are  not  constantly  of  the  same  length.  Time, 
as  measured  by  the  sun,  is  called  apparent  time,  and 
a  clock  so  regulated  as  always  to  keep  exactly  with  the 
sun,  is  said  to  keep  apparent  time.  Mean  time  is  time 
reckoned  by  the  average  length  of  all  the  solar  days 
throughout  the  year.  This  is  the  period  which  consti- 
tutes the  civil  day  of  twenty-four  hours,  beginning  when 
the  sun  is  on  the  lower  meridian,  namely,  at  twelve 
o'clock  at  night,  and  counted  by  twelve  hours  from  the 
lower  to  the  upper  meridian,  and  from  the  upper  to  the 
lower.  The  astronomical  day  is  the  apparent  solar 
day  counted  through  the  whole  twenty-four  hours,  (in- 
stead of  by  periods  of  twelve  hours  each,  as  in  the  civil 
day,)  and  begins  at  noon.  Thus  it  is  now  the  tenth 
of  June,  at  nine  o'clock,  A.  M.,  according  to  civil  time  ; 
but  we  have  not  yet  reached  the  tenth  of  June  by  as- 
tronomical time,  nor  shall  we,  until  noon  to-day ;  con- 
sequently, it  is  now  June  ninth,  twenty-first  hour  of 
astronomical  time.  Astronomers,  since  so  many  of  their 
observations  are  taken  on  the  meridian,  are  always  sup- 
posed to  look  towards  the  south.  Geographers,  having 
formerly  been  conversant  only  with  the  northern  hem- 
isphere, are  always  understood  to  be  looking  towards 
the  north.  Hence,  left  and  right,  when  applied  to  the 
astronomer,  mean  east  and  west,  respectively ;  but  to 
the  geographer  the  right  is  east,  and  the  left,  west. 

Clocks  are  usually  regulated  so  as  to  indicate  mean 
solar  time  ;  yet,  as  this  is  an  artificial  period  not  marked 
off,  like  the  sidereal  day,  by  any  natural  event,  it  is 
necessary  to  know  how  much  is  to  be  added  to,  or  sub- 
tracted from,  the  apparent  solar  time,  in  order  to  give 
the  corresponding  mean  time.  The  interval,  by  which 
apparent  time  differs  from  mean  time,  is  called  the  equa- 
tion of  time.  If  one  clock  is  so  constructed  as  to  keep 
exactly  with  the  sun,  going  faster  or  slower,  according 
as  the  lengths  of  the  solar  days  vary,  and  another  clock 

6  L.  A. 


62  LETTERS  ON  ASTRONOMY. 

is  regulated  to  mean  time,  then  the  difference  of  the 
two  clocks,  at  any  period,  would  be  the  equation  of  time 
for  that  moment.  If  the  apparent  clock  were  faster 
than  the  mean,  then  the  equation  of  time  must  be  sub- 
tracted ;  but  if  the  apparent  clock  were  slower  than  the 
mean,  then  the  equation  of  time  must  be  added,  to  give 
the  mean  time.  The  two  clocks  would  differ  most  about 
the  third  of  November,  when  the  apparent  tirade  is  six- 
teen and  one  fourth  minutes  greater  than  the  mean. 
But  since  apparent  time  is  sometimes  greater  and  some- 
times less  than  mean  time,  the  two  must  obviously  be 
sometimes  equal  to  each  other.  This  is,  in  fact,  the 
case  four  times  a  year,  namely,  April  fifteenth,  June 
fifteenth,  September  first,  and  December  twenty-fourth. 

Astronomical  clocks  are  made  of  the  best  workman- 
ship, with  every  advantage  that  can  promote  their  reg- 
ularity. Although  they  are  brought  to  an  astonishing 
degree  of  accuracy,  yet  they  are  not  as  regular  in  their 
movements  as  the  stars  are,  and  their  accuracy  requires 
to  be  frequently  tested.  The  transit  instrument  itself, 
when  once  accurately  placed  in  the  meridian,  affords 
the  means  of  testing  the  correctness  of  the  clock,  since 
one  revolution  of  a  star,  from  the  meridian  to  the  me- 
ridian again,  ought  to  correspond  exactly  to  twenty-four 
hours  by  the  clock,  and  to  continue  the  same,  from  day 
to  day  ;  and  the  right  ascensions  of  various  stars,  as  they 
cross  the  meridian,  ought  to  be  such  by  the  clock,  as 
they  are  given  in  the  tables,  where  they  are  stated  ac- 
cording to  the  accurate  determinations  of  astronomers. 
Or,  by  taking  the  difference  of  any  two  stars,  on  suc- 
cessive days,  it  will  be  seen  whether  the  going  of  the 
clock  is  uniform  for  that  part  of  the  day  ;  and  by  taking 
the  right  ascensions  of  different  pairs  of  stars,  we  may 
learn  the  rate  of  the  clock  at  various  parts  of  the  day. 
We  thus  learn,  not  only  whether  the  clock  accurately 
measures  the  length  of  the  sidereal  day,  but  also  whether 
it  goes  uniformly  from  hour  to  hour. 

Although  astronomical  clocks  have  been  brought  to 
a  great  degree  of  perfection,  so  as  hardly  to  vary  a  sec- 


TIME  AND  THE  CALENDAR.  ,  63 

ond  for  many  months,  yet  none  are  absolutely  perfect, 
and  most  are  so  far  from  it,  as  to  require  to  be  corrected 
by  means  of  the  transit  instrument,  every  few  days. 
Indeed,  for  the  nicest  observations,  it  is  usual  not  to 
attempt  to  bring  the  clock  to  a  state  of  absolute  correct- 
ness, but,  after  bringing  it  as  near  to  such  a  state  as  can 
conveniently  be  done,  to  ascertain  how  much  it  gains 
or  loses  in  a  day ;  that  is,  to  ascertain  the  rate  of  its 
going,  and  to  make  allowance  accordingly. 

Having  considered  the  manner  in  which  the  smaller 
divisions  of  time  are  measured,  let  us  now  take  a  hasty 
glance  at  the  larger  periods  which  compose  the  calen- 
dar. 

As  a  day  is  the  period  of  the  revolution  of  the  earth 
on  its  axis,  so  a  year  is  the  period  of  the  revolution  of 
the  earth  around  the  sun.  This  time,  which  constitutes 
the  astronomical  year,  has  been  ascertained  with  great 
exactness,  and  found  to  be  three  hundred  and  sixty-five 
days  five  hours  forty-eight  minutes  and  fifty-one  sec- 
onds. The  most  ancient  nations  determined  the  num- 
ber of  days  in  the  year  by  means  of  the  stylus,  a  per- 
pendicular rod  which  casts  its  shadow  on  a  smooth 
plane  bearing  a  meridian  line.  The  time  when  the 
shadow  was  shortest,  would  indicate  the  day  of  the 
Summer  solstice  ;  and  the  number  of  days  which  elaps- 
ed, until  the  shadow  returned  to  the  same  length  again, 
would  show  the  number  of  days  in  the  year.  This  was 
found  to  be  three  hundred  and  sixty-five  whole  days, 
and  accordingly,  this  period  was  adopted  for  the  civil 
year.  Such  a  difference,  however,  between  the  civil 
and  astronomical  years,  at  length  threw  all  dates  into 
confusion.  For  if,  at  first,  the  Summer  solstice  hap- 
pened on  the  twenty-first  of  June,  at  the  end  of  four 
years,  the  sun  would  not  have  reached  the  solstice  until 
the  twenty-second  of  June  ;  that  is,  it  would  have  been 
behind  its  time.  At  the  end  of  the  next  four  years,  the 
solstice  would  fall  on  the  twenty-third ;  and  in  process 
of  time,  it  would  fall  successively  on  every  day  of  the 
year.  The  same  would  be  true  of  any  other  fixed  date. 


64  LETTERS  ON  ASTRONOMY. 

Julius  Caesar,  who  was  distinguished  alike  for  the 
variety  and  extent  of  his  knowledge,  and  his  skill  in 
arms,  first  attempted  to  make  the  calendar  conform  to 
the  motions  of  the  sun. 

"  Amidst  the  hurry  of  tumultuous  war, 

The  stars,  the  gods,  the  heavens,  were  still  his  care." 

Aided  by  Sosigenes,  an  Egyptian  astronomer,  he 
made  the  first  correction  of  the  calendar,  by  introducing 
an  additional  day  every  fourth  year,  making  February 
to  consist  of  twenty-nine  instead  of  twenty-eight  days, 
and  of  course  the  whole  year  to  consist  of  three  hundred 
and  sixty-six  days.  This  fourth  year  was  denominated 
Bissextile,  because  the  sixth  day  before  the  Kalends  of 
March  was  reckoned  twice.  It  is  also  called  Leap  Year. 

The  Julian  year  was  introduced  into  all  the  civilized 
nations  that  submitted  to  the  Roman  power,  and  con- 
tinued in  general  use  until  the  year  1582.  But  the 
true  correction  was  not  six  hours,  but  five  hours  forty- 
nine  minutes ;  hence  the  addition  was  too  great  by 
eleven  minutes.  This  small  fraction  would  amount  in 
one  hundred  years  to  three  fourths  of  a  day,  and  in 
one  thousand  years  to  more  than  seven  days.  From 
the  year  325  to  the  year  1582,  it  had,  in  fact,  amount- 
ed to  more  than  ten  days ;  for  it  was  known  that,  in 
325,  the  vernal  equinox  fell  on  the  twenty-first  of 
March,  whereas,  in  1582,  it  fell  on  the  eleventh.  It 
was  ordered  by  the  Council  of  Nice,  a  celebrated  eccle- 
siastical council,  held  in  the  year  325,  that  Easter  should 
be  celebrated  upon  the  first  Sunday  after  the  first  full 
moon,  next  following  the  vernal  equinox ;  and  as  cer- 
tain other  festivals  of  the  Romish  Church  were  appointed 
at  particular  seasons  of  the  year,  confusion  would  result 
from  such  a  want  of  constancy  between  any  fixed  date 
and  a  particular  season  of  the  year.  Suppose,  for  ex- 
ample, a  festival  accompanied  by  numerous  religious 
ceremonies,  was  decreed  by  the  Church  to  be  held  at 
the  time  when  the  sun  crossed  the  equator  in  the  Spring, 
(an  event  hailed  with  great  joy,  as  the  harbinger  of  the 
return  of  Summer,)  and  that,  in  the  year  325,  March 


TIME  AND  THE   CALENDAR.  ,  65 

twenty-first  was  designated  as  the  time  for  holding  the 
festival,  since,  at  that  period,  it  was  on  the  twenty-first 
of  March  when  the  sun  reached  the  equinox ;  the  next 
year,  the  sun  would  reach  the  equinox  a  little  sooner 
than  the  twenty-first  of  March,  only  eleven  minutes,  in- 
deed, but  still  amounting  in  twelve  hundred  years  to 
ten  days ;  that  is,  in  1582,  the  sun  reached  the  equinox 
on  the  eleventh  of  March.  If,  therefore,  they  should 
continue  to  observe  the  twenty-first  as  a  religious  festival 
in  honor  of  this  event,  they  would  commit  the  absurdity 
of  celebrating  it  ten  days  after  it  had  passed  by.  Pope 
Gregory  the  Thirteenth,  who  was  then  at  the  head  of  the 
Roman  See,  was  a  man  of  science,  and  undertook  to 
reform  the  calendar,  so  that  fixed  dates  would  always 
correspond  to  the  same  seasons  of  the  year.  He  first 
decreed,  that  the  year  should  be  brought  forward  ten 
days,  by  reckoning  the  fifth  of  October  the  fifteenth ; 
and,  in  order  to  prevent  the  calendar  from  falling  into 
confusion  afterwards,  he  prescribed  the  following  rule : 
Every  year  whose  number  is  not  divisible  by  four, 
without  a  remainder,  consists  of  three  hundred  and 
sixty-five  days ;  every  year  which  is  so  divisible,  but 
is  not  divisible  by  one  hundred,  of  three  hundred  and 
sixty-six;  every  year  divisible  by  one  hundred,  but 
not  by  four  hundred,  again,  of  three  hundred  and  six- 
ty-five ;  and  every  year  divisible  by  four  hundred,  of 
three  hundred  and  sixty-six. 

Thus  the  year  1838,  not  being  divisible  by  four,  con- 
tains three  hundred  and  sixty-five  days,  while  1836  and 
1840  are  leap  years.  Yet,  to  make  every  fourth  year 
consist  of  three  hundred  and  sixty-six  days  would  in- 
crease it  too  much,  by  about  three  fourths  of  a  day  in 
a  century ;  therefore  every  hundredth  year  has  only 
three  hundred  and  sixty-five  days.  Thus  1800,  although 
divisible  by  four,  was  not  a  leap  year,  but  a  common 
year.  But  we  have  allowed  a  whole  day  in  a  hundred 
years,  whereas  we  ought  to  have  allowed  only  three 
fourths  of  a  day.  Hence,  in  four  hundred  years,  we 
should  allow  a  day  too  much,  and  therefore,  we  let  the 
6* 


66  LETTERS  ON  ASTRONOMY. 

four  hundredth  remain  a  leap  year.  This  rule  involves 
an  error  of  less  than  a  day  in  four  thousand  two  hun- 
dred and  thirty-seven  years. 

The  Pope,  who,  you  will  recollect,  at  that  age  as- 
sumed authority  over  all  secular  princes,  issued  his  de- 
cree to  the  reigning  sovereigns  of  Christendom,  com- 
manding the  observance  of  the  calendar  as  reformed  by 
him.  The  decree  met  with  great  opposition  among  the 
Protestant  States,  as  they  recognised  in  it  a  new  exer- 
cise of  ecclesiastical  tyranny ;  and  some  of  them,  when 
they  received  it,  made  it  expressly  understood,  that  their 
acquiescence  should  not  be  construed  as  a  submission 
to  the  Papal  authority. 

In  1752,  the  Gregorian  year,  or  New  Style,  was  es- 
tablished in  Great  Britain  by  act  of  Parliament ;  and  the 
dates  of  all  deeds,  and  other  legal  papers,  were  to  be 
made  according  to  it.  As  above  a  century  had  then 
passed  since  the  first  introduction  of  the  new  style,  elev- 
en days  were  suppressed,  the  third  of  September  being 
called  the  fourteenth.  By  the  same  act,  the  begin- 
ning of  the  year  was  changed  from  March  twenty-fifth 
to  January  first.  A  few  persons  born  previously  to 
1752  have  come  down  to  our  day,  and  we  frequently 
see  inscriptions  on  tombstones  of  those  whose  time  of 
birth  is  recorded  in  old  style.  In  order  to  make  this 
correspond  to  our  present  mode  of  reckoning,  we  must 
add  eleven  days  to  the  date.  Thus  the  same  event 
would  be  June  twelfth  of  old  style,  or  June  twenty-third 
of  new  style ;  and  if  an  event  occurred  between  January 
first  and  March  twenty-fifth,  the  date  of  the  year  would 
be  advanced  one,  since  February  1st,  1740,  O.  S.  would 
be  February  1st,  1741,  N.  S.  Thus,  General  Wash- 
ington was  born  February  1 1th,  1731,  O.  S.,  or  February 
22d,  1732,  N.  S.  If  we  inquire  how  any  present  event 
may  be  made  to  correspond  in  date  to  the  old  style, 
we  must  subtract  twelve  days,  and  put  the  year  back 
one,  if  the  event  lies  between  January  first  and  March 
twenty-fifth.  Thus,  June  tenth,  N.  S.  corresponds  to 
May  twenty-ninth,  O.  S. ;  and  March  20th,  1840,  to 


TIME  AND  THE  CALENDAR.  *  67 

March  8th,  1839.  France,  being  a  Roman  Catholic 
country,  adopted  the  new  style  soon  after  it  was  decreed 
by  the  Pope ;  but  Protestant  countries,  as  we  have  seen, 
were  much  slower  in  adopting  it ;  and  Russia,  and  the 
Greek  Church  generally,  still  adhere  to  the  old  style. 
In  order,  therefore,  to  make  the  Russian  dates  corres- 
pond to  ours,  we  must  add  to  them  twelve  days. 

It  may  seem  to  you  very  remarkable,  that  so  much 
pains  should  have  been  bestowed  upon  this  subject ;  but 
without  a  correct  and  uniform  standard  of  time,  the 
dates  of  deeds,  commissions,  and  all  legal  papers ;  of 
fasts  and  festivals,  appointed  by  ecclesiastical  authority  ; 
the  returns  of  seasons,  and  the  records  of  history, — must 
all  fall  into  inextricable  confusion.  To  change  the  ob- 
servance of  certain  religious  feasts,  which  have  been 
long  fixed  to  particular  days,  is  looked  upon  as  an  im- 
pious innovation ;  and  though  the  times  of  the  events, 
upon  which  these  ceremonies  depend,  are  utterly  un- 
known, it  is  still  insisted  upon  by  certain  classes  in 
England,  that  the  Glastenbury  thorn  blooms  on  Christ- 
mas day. 

Although  the  ancient  Grecian  calendar  was  extremely 
defective,  yet  the  common  people  were  entirely  averse 
to  its  reformation.  Their  superstitious  adherence  to 
these  errors  was  satirized  by  Aristophanes,  in  his  com- 
edy of  the  Clouds.  An  actor,  who  had  just  come  from 
Athens,  recounts  that  he  met  with  Diana,  or  the  moon, 
and  found  her  extremely  incensed,  that  they  did  not 
regulate  her  course  better.  She  complained,  that  the 
order  of  Nature  was  changed,  and  every  thing  turned 
topsyturvy.  The  gods  no  longer  knew  what  belonged 
to  them ;  but,  after  paying  their  visits  on  certain  feast- 
days,  and  expecting  to  meet  with  good  cheer,  as  usual, 
they  were  under  the  disagreeable  necessity  of  returning 
back  to  heaven  without  their  suppers. 

Among  the  Greeks,  and  other  ancient  nations,  the 
length  of  the  year  was  generally  regulated  by  the  course 
of  the  moon.  This  planet,  on  account  of  the  different 
appearances  which  she  exhibits  at  her  full,  change,  and 


68  LETTERS  ON  ASTRONOMY. 

quarters,  was  considered  by  them  as  best  adapted  of 
any  of  the  celestial  bodies  for  this  purpose.  As  one 
lunation,  or  revolution  of  the  moon  around  the  earth, 
was  found  to  be  completed  in  about  twenty-nine  and 
one  half  days,  and  twelve  of  these  periods  being  sup- 
posed equal  to  one  revolution  of  the  sun,  their  months 
were  made  to  consist  of  twenty-nine  and  thirty  days  al- 
ternately, and  their  year  of  three  hundred  and  fifty-four 
days.  But  this  disagreed  with  the  annual  revolution 
of  the  sun,  which  must  evidently  govern  the  seasons  of 
the  year,  more  than  eleven  days.  The  irregularities, 
which  such  a  mode  of  reckoning  would  occasion,  must 
have  been  too  obvious  not  to  have  been  observed.  For, 
supposing  it  to  have  been  settled,  at  any  particular  time, 
that  the  beginning  of  the  year  should  be  in  the  Spring ; 
in  about  sixteen  years  afterwards,  the  beginning  would 
have  been  in  Autumn  ;  and  in  thirty-three  or  thirty-four 
years,  it  would  have  gone  backwards  through  all  the 
seasons,  to  Spring  again.  This  defect  they  attempted 
to  rectify,  by  introducing  a  number  of  days,  at  certain 
times,  into  the  calendar,  as  occasion  required,  and  put- 
ting the  beginning  of  the  year  forwards,  in  order  to  make 
it  agree  with  the  course  of  the  sun.  But  as  these  ad- 
ditions, or  intercalations,  as  they  were  called,  were 
generally  consigned  to  the  care  of  the  priests,  who,  from 
motives  of  interest  or  superstition,  frequently  omitted 
them,  the  year  was  made  long  or  short  at  pleasure. 

The  week  is  another  division  of  time,  of  the  highest 
antiquity,  which,  in  almost  all  countries,  has  been  made 
to  consist  of  seven  days ;  a  period  supposed  by  some 
to  have  been  traditionally  derived  from  the  creation  of 
the  world ;  while  others  imagine  it  to  have  been  regu- 
lated by  the  phases  of  the  moon.  The  names,  Satur- 
day, Sunday,  and  Monday,  are  obviously  derived  from 
Saturn,  the  Sun,  and  the  Moon ;  while  Tuesday, 
Wednesday,  Thursday,  and  Friday,  are  the  days  of 
Tuisco,  Woden,  Thor,  and  Friga,  which  are  Saxon 
names  for  Mars,  Mercury,  Jupiter,  and  Venus.* 

*  Bonnycastle's  Astronomy. 


FIGURE   OF  THE  EARTH.        ,  69 

The  common  year  begins  and  ends  on  the  same  day 
of  the  week ;  but  leap  year  ends  one  day  later  than  it 
began.  Fifty- two  weeks  contain  three  hundred  and 
sixty-four  days  ;  if,  therefore,  the  year  begins  on  Tues- 
day, for  example,  we  should  complete  fifty-two  weeks  on 
Monday,  leaving  one  day,  (Tuesday,)  to  complete  the 
year,  and  the  following  year  would  begin  on  Wednes- 
day. Hence,  any  day  of  the  month  is  one  day  later  in 
the  week,  than  the  corresponding  day  of  the  preceding 
year.  Thus,  if  the  sixteenth  of  November,  1838,  falls 
on  Friday,  the  sixteenth  of  November,  1837,  fell  on 
Thursday,  and  will  fall,  in  1839,  on  Saturday.  But  if 
leap  year  begins  on  Sunday,  it  ends  on  Monday,  and 
the  following  year  begins  on  Tuesday  ;  while  any  given 
day  of  the  month  is  two  days  later  in  the  week  than  the 
corresponding  date  of  the  preceding  year. 


LETTER  VII. 

FIGURE  OF  THE  EARTH. 

"  He  took  the  golden  compasses,  prepared 
In  God's  eternal  store,  to  circumscribe 
This  universe,  and  all  created  things  ; 
One  foot  he  centred,  and  the  other  turned 
Round  through  the  vast  profundity  obscure, 
And  said,  '  Thus  far  extend,  thus  far  thy  bounds, 
This  be  thy  just  circumference,  O  World  !'  "—Milton. 

IN  the  earliest  ages,  the  earth  was  regarded  as  one 
continued  plane  ;  but,  at  a  comparatively  remote  period, 
as  five  hundred  years  before  the  Christian  era,  astrono- 
mers began  to  entertain  the  opinion  that  the  earth  is 
round.  We  are  able  now  to  adduce  various  arguments 
which  severally  prove  this  truth.  First,  when  a  ship  is 
coming  in  from  sea,  we  first  observe  only  the  very  high- 
est parts  of  the  ship,  while  the  lower  portions  come  suc- 
cessively into  view.  Were  the  earth  a  continued  plane, 
the  lower  parts  of  the  ship  would  be  visible  as  soon 
as  the  higher,  as  is  evident  from  Fig.  10,  page  70. 


70 


LETTERS  ON  ASTRONOMY. 
Fig.  10. 


Since  light  comes  to  the  eye  in  straight  lines,  by  which 
objects  become  visible,  it  is  evident,  that  no  reason  exists 
why  the  parts  of  the  ship  near  the  water  should  not  be 
seen  as  soon  as  the  upper  parts.  But  if  the  earth  be 
a  sphere,  then  the  line  of  sight  would  pass  above  the 
deck  of  the  ship,  as  is  represented  in  Fig.  1 1  ;  and  as 


the  ship  drew  nearer  to  land,  the  lower  parts  would 
successively  rise  above  this  line  and  come  into  view  ex- 
actly in  the  manner  known  to  observation.  Secondly, 


FIGURE  OF  THE  EARTH.      -  71 

in  a  lunar  eclipse,  which  is  occasioned  by  the  moon's 
passing  through  the  earth's  shadow,  the  figure  of  the 
shadow  is  seen  to  be  spherical,  which  could  not  be  the 
case  unless  the  earth  itself  were  round.  Thirdly,  navi- 
gators, by  steering  continually  in  one  direction,  as  east 
or  west,  have  in  fact  come  round  to  the  point  from 
which  they  started,  and  thus  confirmed  the  fact  of  the 
earth's  rotundity  beyond  all  question.  One  may  also 
reach  a  given  place  on  the  earth,  by  taking  directly  op- 
posite courses.  Thus,  he  may  reach  Canton  in  China, 
by  a  westerly  route  around  Cape  Horn,  or  by  an  east- 
erly route  around  the  Cape  of  Good  Hope.  All  these 
arguments  severally  prove  that  the  earth  is  round. 

But  I  propose,  in  this  Letter,  to  give  you  some  account 
of  the  unwearied  labors  which  have  been  performed  to 
ascertain  the  exact  figure  of  the  earth  ;  for  although  the 
earth  is  properly  described  in  general  language  as  round, 
yet  it  is  not  an  exact  sphere.  Were  it  so,  all  its  diam- 
eters would  be  equal ;  but  it  is  known  that  a  diameter 
drawn  through  the  equator  exceeds  one  drawn  from 
pole  to  pole,  giving  to  the  earth  the  form  of  a  spheroid, 
— a  figure  resembling  an  orange,  where  the  ends  are 
flattened  a  little  and"  the  central  parts  are  swelled  out. 

Although  it  would  be  a  matter  of  very  rational  curi- 
osity, to  investigate  the  precise  shape  of  the  planet  on 
which  Heaven  has  fixed  our  abode,  yet  the  immense 
pains  which  has  been  bestowed  on  this  subject  has  not 
all  arisen  from  mere  curiosity.  No  accurate  measure- 
ments can  be  taken  of  the  distances  and  magnitudes 
of  the  heavenly  bodies,  nor  any  exact  determinations 
made  of  their  motions,  without  a  knowledge  of  the  ex- 
act figure  of  the  earth  ;  and  hence  is  derived  a  power- 
ful motive  for  ascertaining  this  element  with  all  possible 
precision. 

The  first  satisfactory  evidence  that  was  obtained  of 
the  exact  figure  of  the  earth  was  derived  from  reason- 
ing on  the  effects  of  the  earth's  centrifugal  force,  oc- 
casioned by  its  rapid  revolution  on  its  own  axis.  When 
water  is  whirled  in  a  pail,  we  see  it  recede  from  the 


LETTERS  ON  ASTRONOMY. 

centre  and  accumulate  upon  the  sides  of  the  vessel ; 
and  when  a  millstone  is  whirled  rapidly,  since  the  por- 
tions of  the  stone  furthest  from  the  centre  revolve 
much  more  rapidly  than  those  near  to  it,  their  greater 
tendency  to  recede  sometimes  makes  them  fly  off  with 
a  violent  explosion.  A  case,  which  comes  still  nearer 
to  that  of  the  earth,  is  exhibited  by  a  mass  of  clay  re- 
volving on  a  potter's  wheel,  as  seen  in  the  process  of 
making  earthen  vessels.  The  mass  swells  out  in  the 
middle,  in  consequence  of  the  centrifugal  force  exerted 
upon  it  by  a  rapid  motion.  Now,  in  the  diurnal  revo- 
lution, the  equatorial  parts  of  the  earth  move  at  the  rate 
of  about  one  thousand  miles  per  hour,  while  the  poles 
do  not  move  at  all ;  and  since,  as  we  take  points  at 
successive  distances  from  the  equator  towards  the  pole, 
the  rate  at  which  these  points  move  grows  constantly 
less  and  less ;  and  since,  in  revolving  bodies,  the  cen- 
trifugal force  is  proportioned  to  the  velocity,  consequent- 
ly, those  parts  which  move  with  the  greatest  rapidity 
will  be  more  affected  by  this  force  than  those  which 
move  more  slowly.  Hence,  the  equatorial  regions  must 
be  higher  from  the  centre  than  the  polar  regions ;  for, 
were  not  this  the  case,  the  waters  on  the  surface  of  the 
earth  would  be  thrown  towards  the  equator,  and  be 
piled  up  there,  just  as  water  is  accumulated  on  the  sides 
of  a  pail  when  made  to  revolve  rapidly. 

Huyghens,  an  eminent  astronomer  of  Holland,  who 
investigated  the  laws  of  centrifugal  forces,  was  the  first 
to  infer  that  such  must  be  the  actual  shape  of  the  earth ; 
but  to  Sir  Isaac  Newton  we  owe  the  full  developement 
of  this  doctrine.  By  combining  the  reasoning  derived 
from  the  known  laws  of  the  centrifugal  force  with  argu- 
ments derived  from  the  principles  of  universal  gravita- 
tion, he  concluded  that  the  distance  through  the  earth, 
in  the  direction  of  the  equator,  is  greater  than  that  in 
the  direction  of  the  poles.  He  estimated  the  difference 
to  be  about  thirty-four  miles. 

But  it  was  soon  afterwards  determined  by  the  astron- 
omers of  France,  to  ascertain  the  figure  of  the  earth  by 


FIGURE  OF  THE  EARTH.   *  73 

actual  measurements,  specially  instituted  for  that  pur- 
pose. Let  us  see  how  this  could  be  effected.  If  we 
set  out  at  the  equator  and  travel  towards  the  pole,  it  is 
easy  to  see  when  we  have  advanced  one  degree  of  lat- 
itude, for  this  will  be  indicated  by  the  rising  of  the  north 
star,  which  appears  in  the  horizon  when  the  spectator 
stands  on  the  equator,  but  rises  in  the  same  proportion 
as  he  recedes  from  the  equator,  until,  on  reaching  the 
pole,  the  north  star  would  be  seen  directly  over  head. 
Now,  were  the  earth  a  perfect  sphere,  the  meridian  of 
the  earth  would  be  a  perfect  circle,  and  the  distance  be- 
tween any  two  places,  differing  one  degree  in  latitude, 
would  be  exactly  equal  to  the  distance  between  any 
other  two  places,  differing  in  latitude  to  the  same 
amount.  But  if  the  earth  be  a  spheroid,  flattened  at 
the  poles,  then  a  line  encompassing  the  earth  from  north 
to  south,  constituting  the  terrestrial  meridian,  would  not 
be  a  perfect  circle,  but  an  ellipse  or  oval,  having  its 
longer  diameter  through  the  equator,  and  its  shorter 
through  the  poles.  The  part  of  this  curve  included 
between  two  radii,  drawn  from  the  centre  of  the  earth 
to  the  celestial  meridian,  at  angles  one  degree  asunder, 
would  be  greater  in  the  polar  than  in  the  equatorial  re- 
gion ;  that  is,  the  degrees  of  the  meridian  would  length- 
en towards  the  poles. 

The  French  astronomers,  therefore,  undertook  to  as- 
certain by  actual  measurements  of  arcs  of  the  meridian, 
in  different  latitudes,  whether  the  degrees  of  the  merid- 
ian are  of  uniform  length,  or,  if  not,  in  what  manner 
they  differ  from  each  other.  After  several  indecisive 
measurements  of  an  arc  of  the  meridian  in  France,  it 
was  determined  to  effect  simultaneous  measurements  of 
arcs  of  the  meridian  near  the  equator,  and  as  near  as 
possible  to  the  north  pole,  presuming  that  if  degrees  of 
the  meridian,  in  different  latitudes,  are  really  of  different 
lengths,  they  will  differ  most  in  points  most  distant  from 
each  other.  Accordingly,  in  1735,  the  French  Acade- 
my, aided  by  the  government,  sent  out  two  expeditions, 
one  to  Peru  and  the  other  to  Lapland.  Three  distin- 
7  L.  A, 


74  LETTERS  ON   ASTRONOMY. 

guished  mathematicians,  Bouguer,  La  Condamine,  and 
Godin,  were  despatched  to  the  former  place,  and  four 
others,  Maupertius,  Camus,  Clairault,  and  Lemonier, 
were  sent  to  the  part  of  Swedisty  Lapland  which  lies  at 
the  head  of  the  Gulf  of  Tornea,  the  northern  arm  of  the 
Baltic.  This  commission  completed  its  operations  sev- 
eral years  sooner  than  the  other,  which  met  with  great- 
er difficulties  in  the  way  of  their  enterprise.  Still,  the 
northern  detachment  had  great  obstacles  to  contend 
with,  arising  particularly  from  the  extreme  length  and 
severity  of  their  Winters.  The  measurements,  how- 
ever, were  conducted  with  care  and  skill,  and  the  re- 
sult, when  compared  with  that  obtained  for  the  length 
of  a  degree  in  France,  plainly  indicated,  by  its  greater 
amount,  a  compression  of  the  earth  towards  the  poles. 

Mean-while,  Bouguer  and  his  party  were  prosecuting 
a  similar  work  in  Peru,  under  extraordinary  difficulties. 
These  were  caused,  partly  by  the  localities,  and  partly 
by  the  ill-will  and  indolence  of  the  inhabitants.  The 
place  selected  for  their  operations  was  in  an  elevated 
valley  between  two  principal  chains  of  the  Andes.  The 
lowest  point  of  their  arc  was  at  an  elevation  of  a  mile 
and  a  half  above  the  level  of  the  sea ;  and,  in  some  in- 
stances, the  heights  of  two  neighboring  signals  differed 
more  than  a  mile.  Encamped  upon  lofty  mountains, 
they  had  to  struggle  against  storms,  cold,  and  privations 
of  every  description,  while  the  invincible  indifference 
of  the  Indians,  they  were  forced  to  employ,  was  not  to 
be  shaken  by  the  fear  of  punishment  or  the  hope  of  re- 
ward. Yet,  by  patience  and  ingenuity,  they  overcame 
all  obstacles,  and  executed  with  great  accuracy  one  of 
the  most  important  operations,  of  this  nature,  ever  un- 
dertaken. To  accomplish  this,  however,  took  them 
nine  years  ;  of  which,  three  were  occupied  in  determin- 
ing the  latitudes  alone.* 

I  have  recited  the  foregoing  facts,  in  order  to  give  you 
some  idea  of  the  unwearied  pains  which  astronomers 
have  taken  to  ascertain  the  exact  figure  of  the  earth. 

*  Library  of  Useful  Knowledge  :  History  of  Astronomy,  page  95. 


FIGURE  OF  THE  EARTH.      ,  75 

You  will  find,  indeed,  that  all  their  labors  are  charac- 
terized by  the  same  love  of  accuracy.  Years  of  toilsome 
watchings,  and  incredible  labor  of  computation,  have 
been  undergone,  for  the  sake  of  arriving  only  a  few  sec- 
onds nearer  to  the  trutn. 

The  length  of  a  degree  of  the  meridian,  as  measured 
in  Peru,  was  less  than  that  before  determined  in  France, 
and  of  course  less  than  that  of  Lapland ;  so  that  the 
spheroidal  figure  of  the  earth  appeared  now  to  be  ascer- 
tained by  actual  measurement.  Still,  these  measures 
were  too  few  in  number,  and  covered  too  small  a  por- 
tion of  the  whole  quadrant  from  the  equator  to  the  pole, 
to  enable  astronomers  to  ascertain  the  exact  law  of  cur- 
vature of  the  meridian,  and  therefore  similar  measure- 
ments have  since  been  prosecuted  with  great  zeal  by 
different  nations,  particularly  by  the  French  and  English. 
In  1764,  two  English  mathematicians  of  great  emi- 
nence, Mason  and  Dixon,  undertook  the  measurement 
of  an  arc  in  Pennsylvania,  extending  more  than  one 
hundred  miles. 

These  operations  are  carried  on  by  what  is  called  a 
system  of  triangulation.  Without  some  knowledge 
of  trigonometry,  you  will  not  be  able  fully  to  understand 
this  process ;  but,  as  it  is  in  its  nature  somewhat  curious, 
and  is  applied  to  various  other  geographical  measure- 
ments, as  well  as  to  the  determination  of  arcs  of  the 
meridian,  I  am  desirous  that  you  should  understand  its 
general  principles.  Let  us  reflect,  then,  that  it  must 
be  a  matter  of  the  greatest  difficulty,  to  execute  with 
exactness  the  measurement  of  a  line  of  any  great  length 
in  one  continued  direction  on  the  earth's  surface.  Even 
if  we  select  a  level  and  open  country,  more  or  less  ine- 
qualities of  surface  will  occur ;  rivers  must  be  crossed, 
morasses  must  be  traversed,  thickets  must  be  pene- 
trated, and  innumerable  other  obstacles  must  be  sur- 
mounted ;  and  finally,  every  time  we  apply  an  artificial 
measure,  as  a  rod,  for  example,  we  obtain  a  result  not 
absolutely  perfect.  Each  error  may  indeed  be  very 
small,  but  small  errors,  often  repeated,  may  produce  a 


76  LETTERS  ON  ASTRONOMY. 

formidable  aggregate.  Now,  one  unacquainted  with 
trigonometry  can  easily  understand  the  fact,  that,  when 
we  know  certain  parts  of  a  triangle,  we  can  find  the 
other  parts  by  calculation  ;  as,  in  the  rule  of  three  in 
arithmetic,  we  can  obtain  the  fourth  term  of  a  propor- 
tion, from  having  the  first  three  terms  given.  Thus,  in 
the  triangle  ABC,  Fig.  12,  if  we  know  the  side  A  B,  and 
the  angles  at  A  and  B,  we  can  find  by  computation,  the 
other  sides,  A  C  and  B  C,  and  the  remaining  angle  at  C. 
Suppose,  then,  that  in  measuring  an  arc  of  the  meridian 
through  any  country,  the  line  were  to  pass  directly 
Fig.  12.  through  A  B,  but  the  ground  was  so  ob- 
structed between  A  and  B,  that  we  could 
not  possibly  carry  our  measurement 
through  it.  We  might  then  measure 
another  line,  as  A  C,  which  was  accessi- 
ble, and  with  a  compass  take  the  bearing 
of  B  from  the  points  A  and  C,  by  which 
means  we  should  learn  the  value  of  the 
angles  at  A  and  C.  From  these  data  we 
A"  might  calculate,  by  the  rules  of  trigonom- 

etry, the  exact  length  of  the  line  A  B.  Perhaps  the 
ground  might  be  so  situated,  that  we  could  not  reach  the 
point  B,  by  any  route  ;  still,  if  it  could  be  seen  from  A 
and  C,  it  would  be  all  we  should  want.  Thus,  in  con- 
ducting a  trigonometrical  survey  of  any  country,  conspic- 
uous signals  are  placed  on  elevated  points,  and  the  bear- 
ings of  these  are  taken  from  the  extremities  of  a  known 
line,  called  the  base,  and  thus  the  relative  situation  of 
various  places  is  -accurately  determined.  Were  we  to 
undertake  to  run  an  exact  north  and  south  line  through 
any  country,  as  New  England,  we  should  select,  near 
one  extremity,  a  spot  of  ground  favorable  for  actual 
measurement,  as  a  level,  unobstructed  plain  ;  we  should 
provide  a  measure  whose  length  in  feet  and  inches  was 
determined  with  the  greatest  possible  precision,  and 
should  apply  it  with  the  utmost  care.  We  should  thus 
obtain  a  base  line.  From  the  extremities  of  this  line, 
we  should  take  (with  some  appropriate  instrument)  the 


FIGURE  OF  THE  EARTH. 


77 


bearing  of  some  signal  at  a  greater  or  less  distance,  and 
thus  we  should  obtain  one  side  and  two  angles  of  a  tri- 
angle, from  which  we  could  find,  by  the  rules  of  trigo- 
nometry, either  of  the  unknown  sides.  Taking  this  as 
a  new  base,  we  might  take  the  bearing  of  another  sig- 
nal, still  further  on  our  way,  and  thus  proceed  to  run 
the  required  north  and  south  line,  without  actually 
measuring  any  thing  more  than  the  first,  or  base  line. 
Thus,  in  Fig.  13,  we  wish  to  measure  the  distance  be- 
tween the  two  points  A  and  O,  which  are  both  on  the 
same  meridian,  as  is  known  by  their  having  the  same 
longitude ;  but,  on  account  of  Fig.  13. 

various  obstacles,  it  would  be 
found  very  inconvenient  to  mea- 
sure this  line  directly,  with  a  rod 
or  chain,  and  even  if  we  could  do 
it,  we  could  not  by  this  method 
obtain  nearly  so  accurate  a  re- 
sult, as  we  could  by  a  series  of 
triangles,  where,  after  the  base 
line  was  measured,  we  should 
have  nothing  else  to  measure  ex- 
cept angles,  which  can  be  de- 
termined,  by  observation,  to  a 
greater  degree  of  exactness,  than 
lines.  We  therefore,  in  the  first 
place,  measure  the  base  line,  A  B, 
with  the  utmost  precision.  Then, 
taking  the  bearing  of  some  sig- 
nal at  C  from  A  and  B,  we  ob- 
tain  the  means  of  calculating  the  side  B  C,  as  has  been 
already  explained.  Taking  B  C  as  a  new  base,  we  pro- 
ceed, in  like  manner,  to  determine  successively  the  sides 
C  D,  D  E,  and  E  F,  and  also  A  C,  and  C  E.  Although 
A  C  is  not  in  the  direction  of  the  meridian,  but  consid- 
erably to  the  east  of  it,  yet  it  is  easy  to  find  the  cor- 
responding distance  on  the  meridian,  A  M  ;  and  in  the 
same  manner  we  can  find  the  portions  of  the  meridian 
M  N  and  N  O,  corresponding  respectively  to  C  E  and 


78  LETTERS  ON  ASTRONOMY. 

E  F.  Adding  these  several  parts  of  the  meridian  to- 
gether, we  obtain  the  length  of  the  arc  from  A  to  O,  in 
miles ;  and  by  observations  on  the  north  star,  at  each 
extremity  of  the  arc,  namely,  at  A  and  at  O,  we  could 
determine  the  difference  of  latitude  between  these  two 
points.  Suppose,  for  example,  that  the  distance  be- 
tween A  and  O  is  exactly  five  degrees,  and  that  the 
length  of  the  intervening  line  is  three  hundred  and  for- 
ty-seven miles ;  then,  dividing  the  latter  by  the  former 
number,  we  find  the  length  of  a  degree  to  be  sixty- 
nine  miles  and  four  tenths.  To  take,  however,  a  few 
of  the  results  actually  obtained,  they  are  as  follows : 

Ler 


Places  of  observation.  Latitude.  in  mileg 

Peru, 00°  00'  00"  68.732 

Pennsylvania,   ....     39    12   00  68.896 

France, 46    12    00  69.054 

England, 51    29    54J  69.146 

Sweden, 66    20    10  69.292 

This  comparison  shows,  that  the  length  of  a  degree 
gradually  increases,  as  we  proceed  from  the  equator 
towards  the  pole.  Combining  the  results  of  various 
estimates,  the  dimensions  of  the  terrestrial  spheroid  are 
found  to  be  as  follows : 

Equatorial  diameter,     ....  7925.648  miles. 

Polar  diameter, 7899.170     " 

Average  diameter, 7912.409     " 

The  difference  between  the  greatest  and  the  least  is 
about  twenty-six  and  one  half  miles,  which  is  about  one 
two  hundred  and  ninety-ninth  part  of  the  greatest. 
This  fraction  is  denominated  the  ellipticity  of  the  earth, 
— being  the  excess  of  the  equatorial  over  the  polar  di- 
ameter. 

The  operations,  undertaken  for  the  purpose  of  deter- 
mining the  figure  of  the  earth,  have  been  conducted 
with  the  most  refined  exactness.  At  any  stage  of  the 
process,  the  length  of  the  last  side,  as  obtained  by  cal- 
culation, may  be  actually  measured  in  the  same  manner 


FIGURE  OF  THE  EARTH.    »  79 

as  the  base  from  which  the  series  of  triangles  commenc- 
ed. When  thus  measured,  it  is  called  the  base  of  veri- 
fication. In  some  surveys,  the  base  of  verification, 
when  taken  at  a  distance  of  four  hundred  miles  from 
the  starting  point,  has  not  differed  more  than  one  foot 
from  the  same  line,  as  determined  by  calculation. 

Another  method  of  arriving  at  the  exact  figure  of  the 
earth  is,  by  observations  with  the  pendulum.  If  a  pen- 
dulum, like  that  of  a  clock,  be  suspended,  and  the  num- 
ber of  its  vibrations  per  hour  be  counted,  they  will  be 
found  to  be  different  in  different  latitudes.  A  pendulum 
that  vibrates  thirty-six  hundred  times  per  hour,  at  the 
equator,  will  vibrate  thirty-six  hundred  and  five  and  two 
thirds  times,  at  London,  and  a  still  greater  number  of 
times  nearer  the  north  pole.  Now,  the  vibrations  of  the 
pendulum  are  produced  by  the  force  of  gravity.  Hence 
their  comparative  number  at  different  places  is  a  meas- 
ure of  the  relative  forces  of  gravity  at  those  places.  But 
when  we  know  the  relative  forces  of  gravity  at  different 
places,  we  know  their  relative  distances  from  the  centre 
of  the  earth  ;  because  the  nearer  a  place  fs  to  the  centre 
of  the  earth,  the  greater  is  the  force  of  gravity.  Sup- 
pose, for  example,  we  should  count  the  number  of  vi- 
brations of  a  pendulum  at  the  equator,  and  then  carry 
it  to  the  north  pole,  and  count  the  number  of  vibrations 
made  there  in  the  same  time, — we  should  be  able,  from 
these  two  observations,  to  estimate  the  relative  forces 
of  gravity  at  these  two  points  ;  and,  having  the  relative 
forces  of  gravity,  we  can  thence  deduce  their  relative 
distances  from  the  centre  of  the  earth,  and  thus  obtain 
the  polar  and  equatorial  diameters.  Observations  of 
this  kind  have  been  taken  with  the  greatest  accuracy, 
in  many  places  on  the  surface  of  the  earth,  at  various 
distances  from  each  other,  and  they  lead  to  the  same 
conclusions  respecting  the  figure  of  the  earth,  as  those 
derived  from  measuring  arcs  of  the  meridian.  It  is 
pleasing  thus  to  see  a  great  truth,  and  one  apparently 
beyond  the  pale  of  human  investigation,  reached  by  two 
routes  entirely  independent  of  each  other.  Nor,  in- 


80  LETTERS  ON  ASTRONOMY. 

deed,  are  these  the  only  proofs  which  have  been  dis- 
covered of  the  spheroidal  figure  of  the  earth.  In  con- 
sequence of  the  accumulation  of  matter  above  the  equa- 
torial regions  of  the  earth,  a  body  weighs  less  there  than 
towards  the  poles,  being  further  removed  from  the  cen- 
tre of  the  earth.  The  same  accumulation  of  matter, 
by  the  force  of  attraction  which  it  exerts,  causes  slight 
inequalities  in  the  motions  of  the  moon ;  and  since  the 
amount  of  these  becomes  a  measure  of  the  force  which 
produces  them,  astronomers  are  able,  from  these  in- 
equalities, to  calculate  the  exact  quantity  of  the  matter 
thus  accumulated,  and  hence  to  determine  the  figure 
of  the  earth.  The  result  is  not  essentially  different  from 
that  obtained  by  the  other  methods.  Finally,  the  shape 
of  the  earth's  shadow  is  altered,  by  its  spheroidal  figure, 
— a  circumstance  which  affects  the  time  and  duration  of 
a  lunar  eclipse.  All  these  different  and  independent 
phenomena  afford  a  pleasing  example  of  the  harmony 
of  truth.  The  known  effects  of  the  centrifugal  force 
upon  a  body  revolving  on  its  axis,  like  the  earth,  lead 
us  to  infer  that  the  earth  is  of  a  spheroidal  figure  ;  but 
if  this  be  the  fact,  the  pendulum  ought  to  vibrate  faster 
near  the  pole  than  at  the  equator,  because  it  would 
there  be  nearer  the  centre  of  the  earth.  On  trial,  such 
is  found  to  be  the  case.  If,  again,  there  be  such  an 
accumulation  of  matter  about  the  equatorial  regions,  its 
effects  ought  to  be  visible  in  the  motions  of  the  moon, 
which  it  would  influence  by  its  gravity ;  and  there,  also, 
its  effects  are  traced.  At  length,  we  apply  our  meas- 
ures to  the  surface  of  the  earth  itself,  and  find  the  same 
fact,  which  had  thus  been  searched  out  among  the  hid- 
den things  of  Nature,  here  palpably  exhibited  before 
our  eyes.  Finally,  on  estimating  from  these  different 
sources,  what  the  exact  amount  of  the  compression  at 
the  poles  must  be,  all  bring  out  nearly  one  and  the 
same  result.  This  truth,  so  harmonious  in  itself,  takes 
along  with  it,  and  establishes,  a  thousand  other  truths 
on  which  it  rests. 


DIURNAL  REVOLUTIONS.        ,  81 


LETTER  VIII. 

DIURNAL  REVOLUTIONS. 

•'  To  some  she  taught  the  fabric  of  the  sphere, 
The  changeful  moon,  the  circuit  of  the  stars, 
The  golden  zones  of  heaven." — Akenside. 

WITH  the  elementary  knowledge  already  acquired, 
you  will  now  be  able  to  enter  with  pleasure  and  profit 
on  the  various  interesting  phenomena  dependent  on  the 
revolution  of  the  earth  on  its  axis  and  around  the  sun. 
The  apparent  diurnal  revolution  of  the  heavenly  bod- 
ies, from  east  to  west,  is  owing  to  the  actual  revolution 
of  the  earth  on  its  own  axis,  from  west  to  east.  If  we 
conceive  of  a  radius  of  the  earth's  equator  extended 
until  it  meets  the  concave  sphere  of  the  heavens,  then, 
as  the  earth  revolves,  the  extremity  of  this  line  would 
trace  out  a  curve  on  the  face  of  the  sky ;  namely,  the 
celestial  equator.  In  curves  parallel  to  this,  called  the 
circles  of  diurnal  revolution,  the  heavenly  bodies  act- 
ually appear  to  move,  every  star  having  its  own  pecu- 
liar circle.  After  you  have  first  rendered  familiar  the 
real  motion  of  the  earth  from  west  to  east,  you  may 
then,  without  danger  of  misapprehension,  adopt  the 
common  language,  that  all  the  heavenly  bodies  revolve 
around  the  earth  once  a  day,  from  east  to  west,  in  cir- 
cles parallel  to  the  equator  and  to  each  other. 

I  must  remind  you,  that  the  time  occupied  by  a  star, 
in  passing  from  any  point  in  the  meridian  until  it  comes 
round  to  the  same  point  again,  is  called  a  sidereal  day, 
and  measures  the  period  of  the  earth's  revolution  on  its 
axis.  If  we  watch  the  returns  of  the  same  star  from 
day  to  day,  we  shall  find  the  intervals  exactly  equal  to 
each  other ;  that  is,  the  sidereal  days  are  all  equal. 
Whatever  star  we  select  for  the  observation,  the  same 
result  will  be  obtained.  The  stars,  therefore,  always 
keep  the  same  relative  position,  and  have  a  common 


82  LETTERS  ON  ASTRONOMY. 

movement  round  the  earth, — a  consequence  that  natu- 
rally flows  from  the  hypothesis  that  their  apparent  mo- 
tion is  all  produced  by  a  single  real  motion  :  namely,  that 
of  the  earth.  The  sun,  moon,  and  planets,  as  well  as 
the  fixed  stars,  revolve  in  like  manner  ;  but  their  returns 
to  the  meridian  are  not,  like  those  of  the  fixed  stars, 
at  exactly  equal  intervals. 

The  appearances  of  the  diurnal  motions  of  the  heav- 
enly bodies  are  different  in  different  parts  of  the  earth, 
— since  every  place  has  its  own  horizon,  and  different 
horizons  are  variously  inclined  to  each  other.  Noth- 
ing in  astronomy  is  more  apt  to  mislead  us,  than  the 
obstinate  habit  of  considering  the  horizon  as  a  fixed 
and  immutable  plane,  and  of  referring  every  thing  to  it. 
We  should  contemplate  the  earth  as  a  huge  globe,  oc- 
cupying a  small  portion  of  space,  and  encircled  on  all 
sides,  at  an  immense  distance,  by  the  starry  sphere.  We 
should  free  our  minds  from  their  habitual  proneness  to 
consider  one  part  of  space  as  naturally  up  and  another 
down,  and  view  ourselves  as  subject  to  a  force  (gravity) 
which  binds  us  to  the  earth  as  truly  as  though  we  were 
fastened  to  it  by  some  invisible  cords  or  wires,  as  the 
needle  attaches  itself  to  all  sides  of  a  spherical  load- 
stone. We  should  dwell  on  this  point,  until  it  appears 
to  us  as  truly  up,  in  the  direction  B  B,  C  C,  D  D,  when 
one  is  at  B,  C,  D,  respectively,  as  in  the  direction  A  A, 
when  he  is  at  A,  Fig.  14. 

Let  us  now  suppose  the  spectator  viewing  the  diur- 
nal revolutions  from  several  different  positions  on  the 
earth.  On  the  equator,  his  horizon  would  pass  through 
both  poles ;  for  the  horizon  cuts  the  celestial  vault  at 
ninety  degrees  in  every  direction  from  the  zenith  of  the 
spectator ;  but  the  pole  is  likewise  ninety  degrees  from 
his  zenith,  when  he  stands  on  the  equator ;  and  conse- 
quently, the  pole  must  be  in  the  horizon.  Here,  also,  the 
celestial  equator  would  coincide  with  the  prime  vertical, 
being  a  great  circle  passing  through  the  east  and  west 
points.  Since  all  the  diurnal  circles  are  parallel  to  the 
equator,  consequently,  they  would  all,  like  the  equator, 


DIURNAL  REVOLUTIONS.        *  83 

Fiff.  14. 


be  perpendicular  to  the  horizon.  Such  a  view  of  the 
heavenly  bodies  is  called  a  right  sphere,  which  may  be 
thus  defined :  a  right  sphere  is  one  in  which  all  the 
daily  revolutions  of  the  stars  are  in  circles  perpendic- 
ular to  the  horizon. 

A  right  sphere  is  seen  only  at  the  equator.  Any 
star  situated  in  the  celestial  equator  would  appear  to  rise 
directly  in  the  east,  at  midnight  to  be  in  the  zenith  of 
the  spectator,  and  to  set  directly  in  the  west.  In  pro- 
portion as  stars  are  at  a  greater  distance  from  the  equa- 
tor fto wards  the  pole,  they  describe  smaller  and  smaller 
circles,  until,  near  the  pole,  their  motion  is  hardly  per- 
ceptible. 

If  the  spectator  advances  one  degree  from  the  equa- 
tor towards  the  north  pole,  his  horizon  reaches  one  de- 
gree beyond  the  pole  of  the  earth,  and  cuts  the  starry 
sphere  one  degree  below  the  pole  of  the  heavens,  or 
below  the  north  star,  if  that  be  taken  as  the  place  of 
the  pole.  As  he  moves  onward  towards  the  pole,  his 
horizon  continually  reaches  further  and  further  beyond 
it,  until,  when  he  comes  to  the  pole  of  the  earth,  and 
under  the  pole  of  the  heavens,  his  horizon  reaches  on 
all  sides  to  the  equator,  and  coincides  with  it.  More- 


84  LETTERS  ON  ASTRONOMY. 

over,  since  all  the  circles  of  daily  motion  are  parallel  to 
the  equator,  they  become,  to  the  spectator  at  the  pole, 
parallel  to  the  horizon.  Or,  a  parallel  sphere  is  that 
in  which  all  the  circles  of  daily  motion  are  parallel  to 
the  horizon. 

To  render  this  view  of  the  heavens  familiar,  I  would 
advise  you  to  follow  round  in  mind  a  number  of  separ- 
ate stars,  in  their  diurnal  revolution,  one  near  the  hori- 
zon, one  a  few  degrees  above  it,  and  a  third  near  the 
zenith.  To  one  who  stood  upon  the  north  pole,  the 
stars  of  the  northern  hemisphere  would  all  be  perpet- 
ually in  view  when  not  obscured  by  clouds,  or  lost  in  the 
sun's  light,  and  none  of  those  of  the  southern  hemis- 
phere would  ever  be  seen.  The  sun  would  be  con- 
stantly above  the  horizon  for  six  months  in  the  year,  and 
the  remaining  six  continually  out  of  sight.  That  is,  at 
the  pole,  the  days  and  nights  are  each  six  months  long. 
The  appearances  at  the  south  pole  are  similar  to  those 
at  the  north. 

A  perfect  parallel  sphere  can  never  be  seen,  except 
at  one  of  the  poles, — a  point  which  has  never  been  ac- 
tually reached  by  man  ;  yet  the  British  discovery  ships 
penetrated  within  a  few  degrees  of  the  north  pole,  and 
of  course  enjoyed  the  view  of  a  sphere  nearly  parallel. 

As  the  circles  of  daily  motion  are  parallel  to  the  hori- 
zon of  the  pole,  and  perpendicular  to  that  of  the  equa- 
tor, so  at  all  places  between  the  two,  the  diurnal  mo- 
tions are  oblique  to  the  horizon.  This  aspect  of  the 
heavens  constitutes  an  oblique  sphere,  which  is  thus 
defined  :  an  oblique  sphere  is  that  in  which  the  circles 
of  daily  motion  are  oblique  to  the  horizon. 

Suppose,  for  example,  that  the  spectator  is  at  the 
latitude  of  fifty  degrees.  His  horizon  reaches  fifty  de- 
grees beyond  the  pole  of  the  earth,  and  gives  the  same 
apparent  elevation  to  the  pole  of  the  heavens.  It  cuts 
the  equator  and  all  the  circles  of  daily  motion,  at  an 
angle  of  forty  degrees, — being  always  equal  to  what  the 
altitude  of  the  pole  lacks  of  ninety  degrees  ;  that  is,  it 
is  always  equal  to  the  co-altitude  of  the  pole.  Thus, 


DIURNAL  REVOLUTIONS. 


85 


Fig.  15. 


let  H  O,  Fig.  15,  represent  the  horizon,  E  Q,  the  equa- 
tor, and  P  P'  the  axis  of 
the  earth.  Also,  I  Z,  m 
w,  n  w,  parallels  of  lat- 
itude. Then  the  hori- 
zon of  a  spectator  at  Z, 
in  latitude  fifty  degrees, 
reaches  to  fifty  degrees 
beyond  the  pole ;  and 
the  angle  E  C  H,  which 
the  equator  makes  with 
the  horizon,  is  forty 
degrees, — the  comple- 
ment of  the  latitude. 
As  we  advance  still  fur- 
ther north,  the  elevation  of  the  diurnal  circle  above 
the  horizon  grows  less  and  less,  and  consequently,  the 
motions  of  the  heavenly  bodies  more  and  more  oblique 
to  the  horizon,  until  finally,  at  the  pole,  where  the  lati- 
tude is  ninety  degrees,  the  angle  of  elevation  of  the 
equator  vanishes,  and  the  horizon  and  the  equator  co- 
incide with  each  other,  as  before  stated. 

The  circle  of  perpetual  apparition  is  the  boundary 
of  that  space  around  the  elevated  pole,  where  the  stars 
never  set.  Its  distance  from  the  pole  is  equal  to  the 
latitude  of  the  place.  For,  since  the  altitude  of  the 
pole  is  equal  to  the  latitude,  a  star,  whose  polar  distance 
is  just  equal  to  the  latitude,  will,  when  at  its  lowest 
point,  only  just  reach  the  horizon ;  and  all  the  stars 
nearer  the  pole  than  this  will  evidently  not  descend  so 
far  as  the  horizon.  Thus  m  m,  Fig.  15,  is  the  circle  of 
perpetual  apparition,  between  which  and  the  north 
pole,  the  stars  never  set,  and  its  distance  from  the 
pole,  O  P,  is  evidently  equal  to  the  elevation  of  the 
pole,  and  of  course  to  the  latitude. 

In  the  opposite  hemisphere,  a  similar  part  of  the 
sphere  adjacent  to  the  depressed  pole  never  rises. 
Hence,  the  circle  of  perpetual  occultation  is  the  boun- 

8  L.  A. 


86  LETTERS  ON  ASTRONOMY. 

dary  of  that  space  around  the  depressed  pole,  within 
which  the  stars  never  rise. 

Thus  m  m',  Fig.  15,  is  the  circle  of  perpetual  occul- 
tation,  between  which  and  the  south  pole,  the  stars 
never  rise. 

In  an  oblique  sphere,  the  horizon  cuts  the  circles  of 
daily  motion  unequally.  Towards  the  elevated  pole, 
more  than  half  the  circle  is  above  the  horizon,  and  a 
greater  and  greater  portion,  as  the  distance  from  the 
equator  is  increased,  until  finally,  within  the  circle  of 
perpetual  apparition,  the  whole  circle  is  above  the  ho- 
rizon. Just  the  opposite  takes  place  in  the  hemisphere 
next  the  depressed  pole.  Accordingly,  when  the  sun 
is  in  the  equator,  as  the  equator  and  horizon,  like  all 
other  great  circles  of  the  sphere,  bisect  each  other,  the 
days  and  nights  are  equal  all  over  the  globe.  But 
when  the  sun  is  north  of  the  equator,  the  days  become 
longer  than  the  nights,  but  shorter,  when  the  sun  is 
south  of  the  equator.  Moreover,  the  higher  the  lati- 
tude, the  greater  is  the  inequality  in  the  lengths  of  the 
days  and  nights.  By  examining  Fig.  15,  you  will  easi- 
ly see  how  each  of  these  cases  must  hold  good. 

Most  of  the  appearances  of  the  diurnal  revolution 
can  be  explained,  either  on  the  supposition  that  the  ce- 
lestial sphere  actually  turns  around  the  earth  once  in 
twenty-four  hours,  or  that  this  motion  of  the  heavens 
is  merely  apparent,  arising  from  the  revolution  of  the 
earth  on  its  axis,  in  the  opposite  direction, — a  mo- 
tion of  which  we  are  insensible,  as  we  sometimes  lose 
the  consciousness  of  our  own  motion  in  a  ship  or  steam- 
boat, and  observe  all  external  objects  to  be  receding 
from  us,  with  a  common  motion.  Proofs,  entirely  con- 
clusive and  satisfactory,  establish  the  fact,  that  it  is  the 
earth,  and  not  the  celestial  sphere,  that  turns  ;  but  these 
proofs  are  drawn  from  various  sources,  and  one  is  not 
prepared  to  appreciate  their  value,  or  even  to  under- 
stand some  of  them,  until  he  has  made  considerable 
proficiency  in  the  study  of  astronomy,  and  become  fa- 
miliar with  a  great  variety  of  astronomical  phenomena. 


DIURNAL  REVOLUTIONS.  87 

To  such  a  period  we  will  therefore  postpone  the  dis- 
cussion of  the  earth's  rotation  on  its  axis. 

While  we  retain  the  same  place  on  the  earth,  the 
diurnal  revolution  occasions  no  change  in  our  horizon, 
but  our  horizon  goes  round,  as  well  as  ourselves.  Let 
us  first  take  our  station  on  the  equator,  at  sunrise ;  our 
horizon  now  passes  through  both  the  poles  and  through 
the  sun,  which  we  are  to  conceive  of  as  at  a  great  dis- 
tance from  the  earth,  and  therefore  as  cut,  not  by  the 
terrestrial,  but  by  the  celestial,  horizon.  As  the  earth 
turns,  the  horizon  dips  more  and  more  below  the  sun, 
at  the  rate  of  fifteen  degrees  for  every  hour ;  and,  as 
in  the  case  of  the  polar  star,  the  sun  appears  to  rise  at 
the  same  rate.  In  six  hours,  therefore,  it  is  depressed 
ninety  degrees  below  the  sun,  bringing  us  directly  un- 
der the  sun,  which,  for  our  present  purpose,  we  may 
consider  as  having  all  the  while  maintained  the  same 
fixed  position  in  space.  The  earth  continues  to  turn, 
and  in  six  hours  more,  it  completely  "reverses  the  posi- 
tion of  our  horizon,  so  that  the  western  part  of  the  ho- 
rizon, which  at  sunrise  was  diametrically  opposite  to  the 
sun,  now  cuts  the  sun,  and  soon  afterwards  it  rises 
above  the  level  of  the  sun,  and  the  sun  sets.  During 
the  next  twelve  hours,  the  sun  continues  on  the  invisible 
side  of  the  sphere,  until  the  horizon  returns  to  the  po- 
sition from  which  it  set  out,  and  a  new  day  begins. 

Let  us  next  contemplate  the  similar  phenomena  at 
the  poles.  Here  the  horizon,  coinciding,  as  it  does, 
with  the  equator,  would  cut  the  sun  through  its  centre 
and  the  sun  would  appear  to  revolve  along  the  surface 
of  the  sea,  one  half  above  and  the  other  half  below  the 
horizon.  This  supposes  the  sun  in  its  annual  revolution 
to  be  at  one  of  the  equinoxes.  When  the  sun  is  north 
of  the  equator,  it  revolves  continually  round  in  a  circle, 
which,  during  a  single  revolution,  appears  parallel  to 
the  equator,  and  it  is  constantly  day  ;  and  when  the 
sun  is  south  of  the  equator,  it  is,  for  the  same  reason, 
continual  night. 

When  we  have  gained  a  clear  idea  of  the  appear- 


88  LETTERS  ON  ASTRONOMY. 

ances  of  the  diurnal  revolutions,  as  exhibited  to  a  spec- 
tator at  the  equator  and  at  the  pole,  that  is,  in  a  right 
and  in  a  parallel  sphere,  there  will  be  little  difficulty  in 
imagining  how  they  must  be  in  the  intermediate  lati- 
tudes, which  have  an  oblique  sphere. 

The  appearances  of  the  sun  and  stars,  presented  to 
the  inhabitants  of  different  countries,  are  such  as  cor- 
respond to  the  sphere  in  which  they  live.  Thus,  in  the 
fervid  climates  of  India,  Africa,  and  South  America,  the 
sun  mounts  up  to  the  highest  regions  of  the  heavens, 
and  descends  directly  downwards,  suddenly  plunging 
beneath  the  horizon.  His  rays,  darting  almost  vertically 
upon  the  heads  of  the  inhabitants,  strike  with  a  force 
unknown  to  the  people  of  the  colder  climates  ;  while  in 
places  remote  from  the  equator,  as  in  the  north  of  Eu- 
rope, the  sun,  in  Summer,  rises  very  far  in  the  north, 
takes  a  long  circuit  towards  the  south,  and  sets  as  far 
northward  in  the  west  as  the  point  where  it  rose  on 
the  other  side  of  the  meridian.  As  we  go  still  further 
north,  to  the  northern  parts  of  Norway  and  Sweden,  for 
example,  to  the  confines  of  the  frigid  zone,  the  Sum- 
mer's sun  just  grazes  the  northern  horizon,  and  at  noon 
appears  only  twenty-three  and  one  half  degrees  above 
the  southern.  On  the  other  hand,  in  midwinter,  in 
the  north  of  Europe,  as  at  St.  Petersburgh,  the  day 
dwindles  almost  to  nothing, — lasting  only  while  the  sun 
describes  a  very  short  arc  in  the  extreme  south.  In 
some  parts  of  Siberia  and  Iceland,  the  only  day  consists 
of  a  little  glimmering  of  the  sun  on  the  verge  of  the 
southern  horizon,  at  noon. 


PARALLAX  AND  REFRACTION.  89 


LETTER  IX. 

PARALLAX  AND  REFRACTION. 

u  Go,  wondrous  creature  !  mount  where  science  guides, 
Go  measure  earth,  weigh  air,  and  state  the  tides  ; 
Instruct  the  planets  in  what  orbs  to  run, 
Correct  old  Time,  and  regulate  the  sun." — Pope. 

I  THINK  you  must  have  felt  some  astonishment,  that 
astronomers  are  able  to  calculate  the  exact  distances 
and  magnitudes  of  the  sun,  moon,  and  planets.  We 
should,  at  the  first  thought,  imagine  that  such  knowl- 
edge as  this  must  be  beyond  the  reach  of  the  human 
faculties,  and  we  might  be  inclined  to  suspect  that  as- 
tronomers practise  some  deception  in  this  matter,  for 
the  purpose  of  exciting  the  admiration  of  the  unlearn- 
ed. I  will  therefore,  in  the  present  Letter,  endeav- 
or to  give  you  some  clear  and  correct  views  respecting 
the  manner  in  which  astronomers  acquire  this  knowl- 
edge. 

In  our  childhood,  we  all  probably  adopt  the  notion 
that  the  sky  is  a  real  dome  of  definite  surface,  in  which 
the  heavenly  bodies  are  fixed.  When  any  objects  are 
beyond  a  certain  distance  from  the  eye,  we  lose  all 
power  of  distinguishing,  by  our  sight  alone,  between 
different  distances,  and  cannot  tell  whether  a  given  ob- 
ject is  one  million  or  a  thousand  millions  of  miles  off. 
Although  the  bodies  seen  in  the  sky  are  in  fact  at  dis- 
tances extremely  various, — some,  as  the  clouds,  only  a 
few  miles  off;  others,  as  the  moon,  but  a  few  thousand 
miles ;  and  others,  as  the  fixed  stars,  innumerable  mil- 
lions of  miles  from  us, — yet,  as  our  eye  cannot  distin- 
guish these  different  distances,  we  acquire  the  habit  of 
referring  all  objects  beyond  a  moderate  height  to  one 
and  the  same  surface,  namely,  an  imaginary  spherical 
surface,  denominated  the  celestial  vault.  Thus,  the  va- 
rious objects  represented  in  the  diagram  on  next  page, 
though  differing  very  much  in  shape  and  diameter, 
8* 


90  LETTERS  ON  ASTRONOMY. 

would  all  be  projected  upon  the  sky  alike,  and  com- 
pose a  part,  indeed,  of  the  imaginary  vault  itself.  The 
place  which  each  object  occupies  is  determined  by 
lines  drawn  from  the  eye  of  the  spectator  through  the 
extremities  of  the  body,  to  meet  the  imaginary  concave 
sphere.  Thus,  to  a  spectator  at  O,  Fig  16,  the  several 
lines  A  B,  C  D,  and  E  F,  would  all  be  projected  into 

Fig.  16. 


O 

arches  on  the  face  of  the  sky,  and  be  seen  as  parts  of 
the  sky  itself,  as  represented  by  the  lines  A'  B',  C'  D', 
and  E'  F'.  And  were  a  body  actually  to  move  in  the 
several  directions  indicated  by  these  lines,  they  would 
appear  to  the  spectator  to  describe  portions  of  the  ce- 
lestial vault.  Thus,  even  when  moving  through  the 
crooked  line,  from  a  to  6,  a  body  would  appear  to  be 
moving  along  the  face  of  the  sky,  and  of  course  in  a 
regular  curve  line,  from  c  to  d. 

But,  although  all  objects,  beyond  a  certain  moderate 
height,  are  projected  on  the  imaginary  surface  of  the 
sky,  yet  different  spectators  will  project  the  same  ob- 
ject on  different  parts  of  the  sky.  Thus,  a  spectator 
at  A,  Fig.  17,  would  see  a  body,  C,  at  M,  while  a  spec- 
tator at  B  would  see  the  same  body  at  N.  This  change 
of  place  in  a  body,  as  seen  from  different  points,  is  called 
parallax,  which  is  thus  defined :  parallax  is  the  ap- 
parent change  of  place  which  bodies  undergo  by  being 
viewed  from  different  points. 


PARALLAX  AND  REFRACTION.  91 


The  arc  M  N  is  called  the  parallactic  arc,  and  the 
angle  A  C  B,  the  parallactic  angle. 

It  is  plain,  from  the  figure,  that  near  objects  are  much 
more  affected  by  parallax  than  distant  ones.  Thus,  the 
body  C,  Fig.  17,  makes  a  much  greater  parallax  than  the 
more  distant  body  D, — the  former  being  measured  by 
the  arc  M  N,  and  the  latter  by  the  arc  O  P.  We  may 
easily  imagine  bodies  to  be  so  distant,  that  they  would 
appear  projected  at  very  nearly  the  same  point  of  the 
heavens,  when  viewed  from  places  very  remote  from 
each  other.  Indeed,  the  fixed  stars,  as  we  shall  see 
more  fully  hereafter,  are  so  distant,  that  spectators,  a 
hundred  millions  of  miles  apart,  see  each  star  in  one 
and  the  same  place  in  the  heavens. 

It  is  by  means  of  parallax,  that  astronomers  find  the 
distances  and  magnitudes  of  the  heavenly  bodies.  In 
order  fully  to  understand  this  subject,  one  requires  to 
know  something  of  trigonometry,  which  science  ena- 
bles us  to  find  certain  unknown  parts  of  a  triangle  from 
certain  other  parts  which  are  known.  Although  you 
may  not  be  acquainted  with  the  principles  of  trigo- 
nometry, yet  you  will  readily  understand,  from  your 
knowledge  of  arithmetic,  that  from  certain  things  given 
in  a  problem  others  may  be  found.  Every  triangle  has 
of  course  three  sides  and  three  angles ;  and,  if  we  know 


LETTERS   ON  ASTRONOMY. 


Fig.  is. 


two  of  the  angles  and  one  of  the  sides,  we  can  find  all 
the  other  parts,  namely,  the  remaining  angle  and  the 
two  unknown  sides.  Thus,  in  the  triangle  ABC, 
Fig.  18,  if  we  know  the  length  of  the  side  A  B,  and 

how  many  degrees  each 
•i  of  the  angles  ABC  and 
B  C  A  contains,  we  can 
find  the  length  of  the 
side  B  C,  or  of  the  side 
A  C,  and  the  remaining 
angle  at  A.  Now,  let 
us  apply  these  principles 
to  the  measurements  of 
some  of  the  heavenly  bodies. 

In  Fig.  19,  let  A  represent  the  earth,  C  H  the  hori- 
zon, and  H  Z  a  quadrant  of  a  great  circle  of  the  heav- 

Fig.  19. 


ens,  extending  from  the  horizon  to  the  zenith  ;  and 
let  E,  F,  G,  O,  be  successive  positions  of  the  moon,  at 
different  elevations,  from  the  horizon  to  the  meridian. 
Now,  a  spectator  on  the  surface  of  the  earth,  at  A,  would 


PARALLAX  AND  REFRACTION.  93 

refer  the  moon,  when  at  E,  to  h,  on  the  face  of  the  sky, 
whereas,  if  seen  from  the  centre  of  the  earth,  it  would 
appear  at  H.  So,  when  the  moon  was  at  F,  a  specta- 
tor at  A  would  see  it  at  p,  while,  if  seen  from  the  cen- 
tre, it  would  have  appeared  at  P.  The  parallactic  arcs, 
H  h,  P  p,  R  r,  grow  continually  smaller  and  smaller,  as 
a  body  is  situated  higher  above  the  horizon ;  and  when 
the  body  is  in  the  zenith,  then  the  parallax  vanishes  al- 
together, for  at  O  the  moon  would  be  seen  at  Z,  wheth- 
er viewed  from  A  or  C. 

Since,  then,  a  heavenly  body  is  liable  to  be  referred 
to  different  points  on  the  celestial  vault,  when  seen 
from  different  parts  of  the  eaVth,  and  thus  some  confu- 
sion be  occasioned  in  the  determination  of  points  on  the 
celestial  sphere,  astronomers  have  agreed  to  consider 
the  true  place  of  a  celestial  object  to  be  that  where  it 
would  appear,  if  seen  from  the  centre  of  the  earth  ;  and 
the  doctrine  of  parallax  teaches  how  to  reduce  observa- 
tions made  at  any  place  on  the  surface  of  the  earth,  to 
such  as  they  would  be,  if  made  from  the  centre. 

When  the  moon,  or  any  heavenly  body,  is  seen  in  the 
horizon,  as  at  E,  the  change  of  place  is  called  the  hori- 
zontal parallax.  Thus,  the  angle  A  E  C,  measures  the 
horizontal  parallax  of  the  moon.  Were  a  spectator  to 
view  the  earth  from  the  centre  of  the  moon,  he  would 
see  the  semidiameter  of  the  earth  under  this  same  an- 
gle ;  hence,  the  horizontal  parallax  of  any  body  is  the 
angle  subtended  by  the  semidiameter  of  the  earth,  as 
seen  from  the  body.  Please  to  remember  this  fact. 

It  is  evident  from  the  figure,  that  the  effect  of  paral- 
lax upon  the  place  of  a  celestial  body  is  to  depress  it. 
Thus,  in  consequence  of  parallax,  E  is  depressed  by  the 
arc  H  h ;  F,  by  the  arc  P  p  ;  G,  by  the  arc  R  r ;  while 
O  sustains  no  change.  Hence,  in  all  calculations  re- 
specting the  altitude  of  the  sun,  moon,  or  planets,  the 
amount  of  parallax  is  to  be  added :  the  stars,  as  we 
shall  see  hereafter,  have  no  sensible  parallax. 

It  is  now  very  easy  to  see  how,  when  the  parallax 
of  a  body  is  known,  we  may  find  its  distance  from  the 


94 


LETTERS   ON  ASTRONOMY. 


Fig.  20. 


centre  of  the  earth.  Thus,  in  the  triangle  ACE, 
Fig.  19,  the  side  A  C  is  known,  being  the  semidi- 
ameter  of  the  earth ;  the  angle  C  A  E,  being  a  right 
angle,  is  also  known ;  and  the  parallactic  angle,  A  E  C, 
is  found  from  observation ;  and  it  is  a  wellknown  prin- 
ciple of  trigonometry,  that  when  we  have  any  two  an- 
gles of  a  triangle,  we  may  find  the  remaining  angle  by 
subtracting  the  sum  of  these  two  from  one  hundred  and 
eighty  degrees.  Consequently,  in  the  triangle  A  E  C, 
we  know  all  the  angles  and  one  side,  namely,  the  side 
A  C ;  hence,  we  have  the  means  of  finding  the  side 
C  E,  which  is  the  distance  from  the  centre  of  the  earth 
to  the  centre  of  the  moon. 

When  the  distance  of  a  heavenly 
^  *yt  is  known,  and  we  can  measure, 
^  ^instruments,  its  angular  breadth, 
sjcan  easily  determine  its  magni- 
tude. Thus,  if  we  have  the  distance 
of  the  moon,  E  S,  Fig.  20,  and  half 
the  breadth  of  its  disk  S  C,  (which  is 
measured  by  the  angle  S  E  C,)we  can 
find  the  length  of  the  line,  S  C,  in 
miles.  Twice  this  line  is  the  diame- 
ter of  the  body ;  and  when  we  know 
the  diameter  of  a  sphere,  we  can,  by 
wellknown  rules,  find  the  contents 
qf  the  surface,  and  its  solidity. 

You  will  perhaps  be  curious  to 
know,  how  the  moon's  horizontal  parallax  is  found ; 
for  it  must  have  been  previously  ascertained,  before  we 
could  apply  this  method  to  finding  the  distance  of  the 
moon  Jrom  the  earth.  Suppose  that  two  astronomers 
take  their  stations  on  the  same  meridian,  but  one  south 
of  the  equator,  as  at  the  Cape  of  Good  Hope,  and  an- 
other north  of  the  equator,  as  at  Berlin,  in  Prussia,  which 
two  places  lie  nearly  on  the  same  meridian.  The  ob- 
servers would  severally  refer  the  moon  to  different 
points  on  the  face  of  the  sky, — the  southern  observer 
carrying  it  further  north,  and  the  northern  observer  fur- 


PARALLAX  AND  REFRACTION. 


95 


ther  south,  than  its  true  place, 
as  seen  from  the  centre  of  the 
earth.  This  will  be  plain  from 
the  diagram,  Fig.  21.  If  A 
and  B  represent  the  positions 
of  the  spectators,  M  the  moon, 
and  C  D  an  arc  of  the  sky, 
then  it  is  evident,  that  C  D 
would  be  the  parallactic  arc. 

These  observations  furnish 
materials  for  calculating,  by 
the  aid  of  trigonometry,  the 
moon's  horizontal  parallax, 
and  we  have  before  seen  how, 
when  we  know  the  parallax  of  a  h^  <°sph-body,  we  can 
find  both  its  distance  from  the  can  i.'ePt«  ts  magnitude. 

Beside  the  change  of  place  wh.  chese  heavenly 
bodies  undergo,  in  consequence  of  parallax,  there  is 
another,  of  an  opposite  kind,  arising  from  the  effect  of 
the  atmosphere,  called  refraction.  Refraction  elevates 
the  apparent  place  of  a  body,  while  parallax  depresses 
it.  It  affects  alike  the  most  distant  as  well  as  nearer 
bodies. 

In  order  to  understand  the  nature  of  refraction,  we 
must  consider,  that  an  object  always  appears  in  the  di- 
rection in  which  the  last  ray  of  light  comes  to  the  eye. 
If  the  light  which  comes  from  a  star  were  bent  into  fifty 
directions  before  it  reached  the  eye,  the  star  would  nev- 
ertheless appear  in  the  line  described  by  the  ray  nearest 
the  eye.  The  operation  of  this  principle  is  seen  when 
an  oar,  or  any  stick,  is  thrust  into  water.  As  the  rays 
of  light  by  which  the  oar  is  seen  have  their  direction 
changed  as  they  pass  out  of  water  into  air,  the  apparent 
direction  in  wjfiich  the  body  is  seen  is  changed  in  the 
same  degree,  giving  it  a  bent  appearance, — the  part  be- 
low the  water  having  apparently  a  different  direction 
from  the  part  above.  Thus,  in  Fig.  22,  page  96,  if 
S  a  x  be  the  oar,  S  a  b  will  be  the  bent  appearance, 
as  affected  by  refraction.  Thb  transparent  substance 


96 


LETTERS  ON  ASTRONOMY. 
Fig.  22. 


through  whi  ^  any  ray  of  light  passes  is  called  a  medi- 
um. It  is  a  £  >eral  fact  in  optics,  that,  when  light 
passes  out  of  a  i ,  rer  into  a  denser  medium,  as  out  of 
air  into  water,  or  out  of  space  into  air,  it  is  turned 
towards  a  perpendicular  to  the  surface  of  the  medium  ; 
and  when  it  passes  out  of  a  denser  into  a  rarer  medi- 
um, as  out  of  water  into  air,  it  is  turned  from  the  per- 
pendicular. In  the  above  case,  the  light,  passing  out 
of  space  into  air,  is  turned  towards  the  radius  of  the 
earth,  this  being  perpendicular  to  the  surface  of  the  at- 
mosphere ;  and  it  is  turned  more  and  more  towards 
that  radius  the  nearer  it  approaches  to  the  earth,  be- 
cause the  density  of  the  air  rapidly  increases  near  the 
earth. 

Let  us  now  conceive  of  the  atmosphere  as  made  up 
of  a  great  number  of  parallel  strata,  as  A  A,  B  B,  C  C, 
and  D  D,  increasing  rapidly  in  density  (as  is  known  to 
be  the  fact)  in  approaching  near  to  the  surface  of  the 
earth.  Let  S  be  a  star,  from  which  a  ray  of  light,  S  a, 
enters  the  atmosphere  at  a,  where,  being  much  turned 
towards  the  radius  of  the  convex  surface,  it  would 
change  its  direction  into  the  line  a  b,  and  again  into 
b  c,  and  c  O,  reaching  the  eye  at  O.  Now,  since  an 
object  always  appears  in  the  direction  in  which  the 
light  finally  strikes  the  eye,  the  star  would  be  seen  in 
the  direction  O  c,  and,  consequently,  the  star  would 


PARALLAX  AND  REFRACTION.  97 

apparently  change  its  place,  by  refraction,  from  S  to  S', 
being  elevated  out  of  its  true  position.  Moreover,  since, 
on  account  of  the  continual  increase  of  density  in  de- 
scending through  the  atmosphere,  the  light  would  be 
continually  turned  out  of  its  course  more  and  more,  it 
would  therefore  move,  not  in  the  polygon  represented  in 
the  figure,  but  in  a  corresponding  curve  line,  whose  cur- 
vature is  rapidly  increased  near  the  surface  of  the  earth. 

When  a  body  is  in  the  zenith,  since  a  ray  of  light 
from  it  enters  the  atmosphere  at  right  angles  to  the  re- 
fracting medium,  it  suffers  no  refraction.  Consequent- 
ly, the  position  of  the  heavenly  bodies,  when  in  the 
zenith,  is  not  changed  by  refraction,  while,  near  the 
horizon,  where  a  ray  of  light  strikes  the  medium  very 
obliquely,  and  traverses  the  atmosphere  through  its 
densest  part,  the  refraction  is  greatest.  The  whole 
amount  of  refraction,  when  a  body  is  in  the  horizon,  is 
thirty-four  minutes ;  while,  at  only  an  elevation  of  one 
degree,  the  refraction  is  but  twenty-four  minutes ;  and  at 
forty-five  degrees,  it  is  scarcely  a  single  minute.  Hence 
it  is  always  important  to  make  our  observations  on  the 
heavenly  bodies  when  they  are  at  as  great  an  elevation 
as  possible  above  the  horizon,  being  then  less  affected 
by  refraction  than  at  lower  altitudes. 

Since  the  whole  amount  of  refraction  near  the  horizon 
exceeds  thirty-three  minutes,  and  the  diameters  of  the 
sun  and  moon  are  severally  less  than  this,  these  lumina- 
ries are  in  view  both  before  they  have  actually  risen  and 
after  they  have  set. 

The  rapid  increase  of  refraction  near  the  horizon  is 
strikingly  evinced  by  the  oval  figure  which  the  sun  as- 
sumes when  near  the  horizon,  and  which  is  seen  to  the 
greatest  advantage  when  light  clouds  enable  us  to  view 
the  solar  disk.  Were  all  parts  of  the  sun  equally  raised 
by  refraction,  there  would  be  no  change  of  figure  ;  but, 
since  the  lower  side  is  more  refracted  than  the  upper,  the 
effect  is  to  shorten  the  vertical  diameter,  and  thus  to 
give  the  disk  an  oval  form.  This  effect  is  particularly 
remarkable  when  the  sun,  at  his  rising  or  setting,  is  ob- 

9  L.  A. 


98  LETTERS  ON  ASTRONOMY. 

served  from  the  top  of  a  mountain,  or  at  an  elevation 
near  the  seashore ;  for  in  such  situations,  the  rays  of 
light  make  a  greater  angle  than  ordinary  with  a  perpen- 
dicular to  the  refracting  medium,  and  the  amount  of 
refraction  is  proportionally  greater.  In  some  cases  of 
this  kind,  the  shortening  of  the  vertical  diameter  of  the 
sun  has  been  observed  to  amount  to  six  minutes,  or 
about  one  fifth  of  the  whole. 

The  apparent  enlargement  of  the  sun  and  moon, 
when  near  the  horizon,  arises  from  an  optical  illusion. 
These  bodies,  in  fact,  are  not  seen  under  so  great  an 
angle  when  in  the  horizon  as  when  on  the  meridian,  for 
they  are  nearer  to  us  in  the  latter  case  than  in  the  for- 
mer. The  distance  of  the  sun,  indeed,  is  so  great,  that 
it  makes  very  little  difference  in  his  apparent  diameter 
whether  he  is  viewed  in  the  horizon  or  on  the  meridi- 
an ;  but  with  the  moon,  the  case  is  otherwise  ;  its  angu- 
lar diameter,  when  measured  with  instruments,  is  per- 
ceptibly larger  when  at  its  culmination,  or  highest  ele- 
vation above  the  horizon.  Why,  then,  do  the  sun  and 
moon  appear  so  much  larger  when  near  the  horizon  ? 
It  is  owing  to  a  habit  of  the  mind,  by  which  we  judge 
of  the  magnitudes  of  distant  objects,  not  merely  by  the 
angle  they  subtend  at  the  eye,  but  also  by  our  impres- 
sions respecting  their  distance,  allowing,  under  a  given 
angle,  a  greater  magnitude  as  we  imagine  the  distance 
of  a  body  to  be  greater.  Now,  on  account  of  the  nu- 
merous objects  usually  in  sight  between  us  and  the  sun, 
when  he  is  near  the  horizon,  he  appears  much  further 
removed  from  us  than  when  on  the  meridian  ;  and  we 
unconsciously  assign  to  him  a  proportionally  greater 
magnitude.  If  we  view  the  sun,  in  the  two  positions, 
through  a  smoked  glass,  no  such  difference  of  size  is 
observed  ;  for  here  no  objects  are  seen  but  the  sun  him- 
self. 

Twilight  is  another  phenomenon  depending  on  the 
agency  of  the  earth's  atmosphere.  It  is  that  illumina- 
tion of  the  sky  which  takes  place  just  before  sunrise, 
and  which  continues  after  sunset.  It  is  owing  partly 


PARALLAX  AND  REFRACTION.  99 

to  refraction,  and  partly  to  reflection,  but  mostly  to  the 
latter.  While  the  sun  is  within  eighteen  degrees  of  the 
horizon,  before  it  rises  or  after  it  sets,  some  portion  of 
its  light  is  conveyed  to  us,  by  means  of  numerous  re- 
flections from  the  atmosphere.  At  the  equator,  where 
the  circles  of  daily  motion  are  perpendicular  to  the  ho- 
rizon, the  sun  descends  through  eighteen  degrees  in  an 
hour  and  twelve  minutes.  The  light  of  day,  therefore, 
declines  rapidly,  and  as  rapidly  advances  after  daybreak 
in  the  morning.  At  the  pole,  a  constant  twilight  is 
enjoyed  while  the  sun  is  within  eighteen  degrees  of  the 
horizon,  occupying  nearly  two  thirds  of  the  half  year 
when  the  direct  light  of  the  sun  is  withdrawn,  so  that 
the  progress  from  continual  day  to  constant  night  is 
exceedingly  gradual.  To  an  inhabitant  of  an  oblique 
sphere,  the  twilight  is  longer  in  proportion  as  the  place 
is  nearer  the  elevated  pole. 

Were  it  not  for  the  power  the  atmosphere  has  of 
dispersing  the  solar  light,  and  scattering  it  in  various 
directions,  no  objects  would  be  visible  to  us  out  of  di- 
rect sunshine  ;  every  shadow  of  a  passing  cloud  would 
involve  us  in  midnight  darkness ;  the  stars  would  be 
visible  all  day  ;  and  every  apartment  into  which  the  sun 
had  not  direct  admission  would  be  involved  in  the  ob- 
scurity of  night.  This  scattering  action  of  the  atmos- 
phere on  the  solar  light  is  greatly  increased  by  the  ir- 
regularity of  temperature  caused  by  the  sun,  which 
throws  the  atmosphere  into  a  constant  state  of  undula- 
tion ;  and  by  thus  bringing  together  masses  of  air  of 
different  temperatures,  produces  partial  reflections  and 
refractions  at  their  common  boundaries,  by  which  means 
much  light  is  turned  aside  from  a  direct  course,  and  di- 
verted to  the  purposes  of  general  illumination.*  In  the 
upper  regions  of  the  atmosphere,  as  on  the  tops  of  very 
high  mountains,  where  the  air  is  too  much  rarefied  to 
reflect  much  light,  the  sky  assumes  a  black  appearance, 
and  stars  become  visible  in  the  day  time. 

Although  the  atmosphere  is  usually  so  transparent, 

*  Sir  J.  Herschel. 


100  LETTERS  ON  ASTRONOMY. 

that  it  is  invisible  to  us,  yet  we  as  truly  move  and  live 
in  a  fluid  as  fishes  that  swim  in  the  sea.  Considered  in 
comparison  with  the  whole  earth,  the  atmosphere  is  to 
be  regarded  as  a  thin  layer  investing  the  surface,  like 
a  film  of  water  covering  the  surface  of  an  orange.  Its 
actual  height,  however,  is  over  a  hundred  miles,  though 
we  cannot  assign  its  precise  boundaries.  Being  per- 
fectly elastic,  the  lower  portions,  bearing  as  they  do, 
the  weight  of  all  the  mass  above  them,  are  greatly 
compressed,  while  the  upper  portions  having  little  to 
oppose  the  natural  tendency  of  air  to  expand,  diffuse 
themselves  widely.  The  consequence  is,  that  the  at- 
mosphere undergoes  a  rapid  diminution  of  density,  as 
we  ascend  from  the  earth,  and  soon  becomes  exceed- 
ingly rare.  At  so  moderate  a  height  as  seven  miles,  it 
is  four  times  rarer  than  at  the  surface,  and  continues  to 
grow  rare  in  the  same  proportion,  namely,  being  four 
times  less  for  every  seven  miles  of  ascent.  It  is  only, 
therefore,  within  a  few  miles  of  the  earth,  that  the  at- 
mosphere is  sufficiently  dense  to  sustain  clouds  and  va- 
pors, which  seldom  rise  so  high  as  eight  miles,  and  are 
usually  much  nearer  to  the  earth  than  this.  So  rare 
does  the  air  become  on  the  top  of  Mount  Chimborazo, 
in  South  America,  that  it  is  incompetent  to  support 
most  of  the  birds  that  fly  near  the  level  of  the  sea. 
The  condor,  a  bird  which  has  remarkably  long  wings, 
and  a  light  body,  is  the  only  bird  seen  towering  above 
this  lofty  summit.  The  transparency  of  the  atmos- 
phere,— a  quality  so  essential  to  fine  views  of  the  starry 
heavens, — is  much  increased  by  containing  a  large  pro- 
portion of  water,  provided  it  is  perfectly  dissolved,  or  in 
a  state  of  invisible  vapor.  A  country  at  once  hot  and 
humid,  like  some  portions  of  the  torrid  zone,  presents  a 
much  brighter  and  more  beautiful  view  of  the  moon 
and  stars,  than  is  seen  in  cold  climates.  Before  a  co- 
pious rain,  especially  in  hot  weather,  when  the  atmos- 
phere is  unusually  humid,  we  sometimes  observe  the  sky 
to  be  remarkably  resplendent,  even  in  our  own  latitude. 
Accordingly,  this  unusual  clearness  of  the  sky,  when 


THE   SUN.  101 

the  stars  shine  with  unwonted  brilliancy,  is  regarded  as 
a  sign  of  approaching  rain ;  and  when,  after  the  rain 
is  apparently  over,  the  air  is  remarkably  transparent, 
and  distant  objects  on  the  earth  are  seen  with  uncom- 
mon distinctness,  while  the  sky  exhibits  an  unusually 
deep  azure,  we  may  conclude  that  the  serenity  is  only 
temporary,  and  that  the  rain  will  probably  soon  return. 


LETTER  X. 

THE  SUN. 

"  Great  source  of  day  !  best  image  here  below 
Of  thy  Creator,  ever  pouring  wide, 
From  world  to  world,  the  vital  ocean  round, 
On  Nature  write,  with  every  beam,  His  praise."— Thomson. 

THE  subjects  which  have  occupied  the  preceding 
Letters  are  by  no  means  the  most  interesting  parts  of 
our  science.  They  constitute,  indeed,  little  more  than 
an  introduction  to  our  main  subject,  but  comprise  such 
matters  as  are  very  necessary  to  be  clearly  understood, 
before  one  is  prepared  to  enter  with  profit  and  delight 
upon  the  more  sublime  and  interesting  field  which  now 
opens  before  us. 

We  will  begin  our  survey  of  the  heavenly  bodies 
with  the  SUN,  which  first  claims  our  homage,  as  the 
natural  monarch  of  the  skies.  The  moon  will  next  oc- 
cupy our  attention ;  then  the  other  bodies  which  com- 
pose the  solar  system,  namely,  the  planets  and  comets ; 
and,  finally,  we  shall  leave  behind  this  little  province 
in  the  great  empire  of  Nature,  and  wing  a  bolder  flight 
to  the  fixed  stars. 

The  distance  of  the  sun  from  the  earth  is  about 
ninety-five  millions  of  miles.  It  may  perhaps  seem  in- 
credible to  you,  that  astronomers  should  be  able  to  de- 
termine this  fact  with  any  degree  of  certainty.  Some, 
indeed,  not  so  well  informed  as  yourself,  have  looked 
upon  the  marvellous  things  that  are  told  respecting  the 
9* 


102  LETTERS  ON  ASTRONOMY. 

distances,  magnitudes,  and  velocities,  of  the  heavenly 
bodies,  as  attempts  of  astronomers  to  impose  on  the 
credulity  of  the  world  at  large ;  but  the  certainty  and 
exactness  with  which  the  predictions  of  astronomers 
are  fulfilled,  as  an  eclipse,  for  example,  ought  to  inspire 
full  confidence  in  their  statements.  I  can  assure  you, 
my  dear  friend,  that  the  evidence  on  which  these  state- 
ments are  founded  is  perfectly  satisfactory  to  those 
whose  attainments  in  the  sciences  qualify  them  to  un- 
derstand them  ;  and,  so  far  are  astronomers  from  wish- 
ing to  impose  on  the  unlearned,  by  announcing  such 
wonderful  discoveries  as  they  have  made  among  the 
heavenly  bodies,  no  class  of  men  have  ever  shown  a 
stricter  regard  and  zeal  than  they  for  the  exact  truth, 
wherever  it  is  attainable. 

Ninety-five  millions  of  miles  is  indeed  a  vast  distance. 
No  human  mind  is  adequate  to  comprehend  it  fully  ; 
but  the  nearest  approaches  we  can  make  towards  it  are 
gained  by  successive  efforts  of  the  mind  to  conceive  of 
great  distances,  beginning  with  such  as  are  clearly  with- 
in our  grasp.  Let  us,  then,  first  take  so  small  a  distance 
as  that  of  the  breadth  of  the  Atlantic  ocean,  and  follow,  in 
mind,  a  ship,  as  she  leaves  the  port  of  New  York,  and, 
after  twenty  days'  steady  sail,  reaches  Liverpool.  Hav- 
ing formed  the  best  idea  we  are  able  of  this  distance, 
we  may  then  reflect,  that  it  would  take  a  ship,  moving 
constantly  at  the  rate  of  ten  miles  per  hour,  more  than 
a  thousand  years  to  reach  the  sun. 

The  diameter  of  the  sun  is  towards  a  million  of 
miles  ;  or,  more  exactly,  it  is  eight  hundred  and  eighty- 
five  thousand  miles.  One  hundred  and  twelve  bodies 
as  large  as  the  earth,  lying  side  by  side,  would  be  re- 
quired to  reach  across  the  solar  disk  ;  and  our  ship, 
sailing  at  the  same  rate  as  before,  would  be  ten  years 
in  passing  over  the  same  space.  Immense  as  is  the 
sun,  we  can  readily  understand  why  it  appears  no 
larger  than  it  does,  when  we  reflect,  that  its  distance  is 
still  more  vast.  Even  large  objects  on  the  earth,  when 
seen  on  a  distant  eminence,  or  over  a  wide  expanse  of 


THE  SUN.  103 

water,  dwindle  almost  to  a  point.  Could  we  approach 
nearer  and  nearer  to  the  sun,  it  would  constantly  ex- 
pand its  volume,  until  finally  it  would  fill  the  whole 
vault  of  heaven.  We  could,  however,  approach  but 
little  nearer  to  the  sun  without  being  consumed  by  the 
intensity  of  his  heat.  Whenever  we  come  nearer  to 
any  fire,  the  heat  rapidly  increases,  being  four  times  as 
great  at  half  the  distance,  and  one  hundred  times  as 
great  at  one  tenth  the  distance.  This  fact  is  expressed 
by  saying,  that  the  heat  increases  as  the  square  of  the 
distance  decreases.  Our  globe  is  situated  at  such  a 
distance  from  the  sun,  as  exactly  suits  the  animal  and 
vegetable  kingdoms.  Were  it  either  much  nearer  or 
much  more  remote,  they  could  not  exist,  constituted  as 
they  are.  The  intensity  of  the  solar  light  also  follows 
the  same  law.  Consequently,  were  we  nearer  to  the  sun 
than  we  are,  its  blaze  would  be  insufferable ;  or,  were 
we  much  further  off,  the  light  would  be  too  dim  to 
serve  all  the  purposes  of  vision. 

The  sun  is  one  million  four  hundred  thousand  times 
as  large  as  the  earth ;  but  its  matter  is  not  more  than 
about  one  fourth  as  dense  as  that  of  the  earth,  being 
only  a  little  heavier  than  water,  while  the  average  den- 
sity of  the  earth  is  more  than  five  times  that  of  water. 
Still,  on  account  of  the  immense  magnitude  of  the  sun, 
its  entire  quantity  of  matter  is  three  JMpndred  and  fifty 
thousand  times  as  great  as  that  of  the  earth.  Now,  the 
force  of  gravity  in  a  body  is  greater,  in  proportion  as 
its  quantity  of  matter  is  greater.  Consequently,  we 
might  suppose,  that  the  weight  of  a  body  (weight  being 
nothing  else  than  the  measure  of  the  force  of  gravity) 
would  be  increased  in  the  same  proportion ;  or,  that  a 
body,  which  weighs  only  one  pound  at  the  surface  of 
the  earth,  would  weigh  three  hundred  and  fifty  thous- 
and pounds  at  the  sun.  But  we  must  consider,  that  the 
attraction  exerted  by  any  body  is  the  same  as  though  all 
the  matter  were  concentrated  in  the  centre.  Thus,  the 
attraction  exerted  by  the  earth  and  by  the  sun  is  the 
same  as  though  the  entire  matter  of  each  body  were 


104  LETTERS  ON  ASTRONOMY. 

in  its  centre.  Hence,  on  account  of  the  vast  dimen- 
sions of  the  sun,  its  surface  is  one  hundred  and  twelve 
times  further  from  its  centre  than  the  surface  of  the 
earth  is  from  its  centre  ;  and,  since  the  force  of  gravi- 
ty diminishes  as  the  square  of  the  distance  increases, 
that  of  the  sun,  exerted  on  bodies  at  its  surface,  is  (so 
far  as  this  cause  operates)  the  square  of  one  hundred 
and  twelve,  or  twelve  thousand  five  hundred  and  for- 
ty-four times  less  than  that  of  the  earth.  If,  there- 
fore, we  increase  the  weight  of  a  body  three  hundred 
and  fifty-four  thousand  times,  in  consequence  of  the 
greater  amount  of  matter  in  the  sun,  and  diminish  it 
twelve  thousand  five  hundred  and  forty-four  times,  in 
consequence  of  the  force  acting  at  a  greater  distance 
from  the  body,  we  shall  find  that  the  body  would  weigh 
about  twenty-eight  times  more  on  the  sun  than  on  the 
earth.  Hence,  a  man  weighing  three  hundred  pounds 
would,  if  conveyed  to  the  surface  of  the  sun,  weigh 
eight  thousand  four  hundred  pounds,  or  nearly  three 
tons  and  three  quarters.  A  limb  of  our  bodies,  weigh- 
ing forty  pounds,  would  require  to  lift  it  a  force  of  one 
thousand  one  hundred  and  twenty  pounds,  which  would 
be  beyond  the  ordinary  power  of  the  muscles.  At  the 
surface  of  the  earth,  a  body  falls  from  rest  by  the  force 
of  gravity,  in  one  second,  sixteen  and  one  twelfth  feet ; 
but  at  the  surface  of  the  sun,  a  body  would,  in  the  same 
time,  fall  througn  four  hundred  and  forty-eight  and 
seven  tenths  feet. 

The  sun  turns  on  his  own  axis  once  in  a  little  more 
than  twenty-five  days.  This  fact  is  known  by  observing 
certain  dark  places  seen  by  the  telescope  on  the  sun's 
disk,  called  solar  spots.  These  are  very  variable  in 
size  and  number.  Sometimes,  the  sun's  disk,  when 
viewed  with  a  telescope,  is  quite  free  from  spots,  while 
at  other  times  we  may  see  a  dozen  or  more  distinct 
clusters,  each  containing  a  great  number  of  spots,  some 
large  and  some  very  minute.  Occasionally,  a  single 
spot  is  so  large  as  to  be  visible  to  the  naked  eye,  es- 
pecially when  the  sun  is  near  the  horizon,  and  the  glare 


THE   SUN.  105 

of  his  light  is  taken  off.  One  measured  by  Dr.  Herschel 
was  no  less  than  fifty  thousand  miles  in  diameter.  A 
solar  spot  usually  consists  of  two  parts,  the  nucleus  and 
the  umbra.  The  nucleus  is  black,  of  a  very  irregular 
shape,  and  is  subject  to  great  and  sudden  changes,  both 
in  form  and  size.  Spots  have  sometimes  seemed  to 
burst  asunder,  and  to  project  fragments  in  different  di- 
rections. The  umbra  is  a  wide  margin,  of  lighter  shade, 
and  is  often  of  greater  extent  than  the  nucleus.  The 
spots  are  usually  confined  to  a  zone  extending  across 
the  central  regions  of  the  sun,  not  exceeding  sixty  de- 
Fig  23  grees  in  breadth.  Fig. 

23  exhibits  the  appear- 
ance of  the  solar  spots. 
As  these  spots  have  all  a 
common  motion  from  day 
to  day,  across  the  sun's 
disk ;  as  they  go  off  at 
one  limb,  and,  after  a  cer- 
tain interval,  sometimes 
come  on  again  on  the  op- 
posite limb,  it  is  inferred 
that  this  apparent  motion 
is  imparted  to  them  by 
an  actual  revolution  of  the  sun  on  his  own  axis.  We 
know  that  the  spots  must  be  in  contact,  or  very  nearly  so, 
at  least,  with  the  body  of  the  sun,  and  cannot  be  bodies 
revolving  around  it,  which  are  projected  on  the  solar  disk 
when  they  are  between  us  and  the  sun  ;  for,  in  that 
case,  they  would  not  be  so  long  in  view  as  out  of  view, 
as  will  be  evident  from  inspecting  the  following  dia- 
gram. Let  S,  Fig.  24,  page  106,  represent  the  sun, 
and  b  a  body  revolving  round  it  in  the  orbit  a  b  c  ; 
and  let  E  represent  the  earth,  where,  of  course,  the 
spectator  is  situated.  The  body  would  be  seen  pro- 
jected on  the  sun  only  while  passing  from  b  to  c,  while, 
throughout  the  remainder  of  its  orbit,  it  would  be  out 
of  view,  whereas  no  such  inequality  exists  in  respect  to 
the  two  periods. 


106 


LETTERS   ON  ASTRONOMY. 


If  you  ask,  what  is  the  cause 
of  the  solar  spots,  I  can  only  tell 
you  what  different  astronomers 
have  supposed  respecting  them. 
They  attracted  the  notice  of 
Galileo  soon  after  the  invention 
of  the  telescope,  and  he  formed 
an  hypothesis  respecting  their 
nature.  Supposing  the  sun  to 
consist  of  a  solid  body  embosom- 
ed in  a  sea  of  liquid  fire,  he 
believed  that  the  spots  are  com- 
posed of  black  cinders,  formed 
in  the  interior  of  the  sun  by  vol- 
canic action,  which  rise  and  float 
on  the  surface  of  the  fiery  sea. 
The  chief  objections  to  this  hy- 
pothesis are,  first,  the  vast  extent 
of  some  of  the  spots,  covering, 
as  they  do,  two  thousand  mil- 
lions of  square  miles,  or  more, — a 
space  which  it  is  incredible  should  be  filled  by  lava  in 
so  short  a  time  as  that  in  which  the  spots  are  sometimes 
formed ;  and,  secondly,  the  sudden  disappearance  which 
the  spots  sometimes  undergo,  a  fact  which  can  hardly 
be  accounted  for  by  supposing,  as  Galileo  did,  that  such 
a  vast  accumulation  of  matter  all  at  once  sunk  beneath 
the  fiery  flood.  Moreover,  we  have  many  reasons  for 
believing  that  the  spots  are  depressions  below  the  gen- 
eral surface. 

La  Lande,  an  eminent  French  astronomer  of  the  last 
century,  held  that  the  sun  is  a  solid,  opaque  body,  hav- 
ing its  exterior  diversified  with  high  mountains  and  deep 
valleys,  and  covered  all  over  with  a  burning  sea  of  liquid 
matter.  The  spots  he  supposed  to  be  produced  by  the 
flux  and  reflux  of  this  fiery  sea,  retreating  occasionally 
from  the  mountains,  and  exposing  to  view  a  portion  of 
the  dark  body  of  the  sun.  But  it  is  inconsistent  with 
the  nature  of  fluids,  that  a  liquid,  like  the  sea  supposed, 


THE   SUN.  107 

should  depart  so  far  from  its  equilibrium  and  remain  so 
long  fixed,  as  to  lay  bare  the  immense  spaces  occupied 
by  some  of  the  solar  spots. 

Dr.  Herschel's  views  respecting  the  nature  and  con- 
stitution of  the  sun,  embracing  an  explanation  of  the 
solar  spots,  have,  of  late  years,  been  very  generally  re- 
ceived by  the  astronomical  world.  This  great  astrono- 
mer, after  attentively  viewing  the  surface  of  the  sun,  for 
a  long  time,  with  his  large  telescopes,  came  to  the  fol- 
lowing conclusions  respecting  the  nature  of  this  lumi- 
nary. He  supposes  the  sun  to  be  a  planetary  body  like 
our  earth,  diversified  with  mountains  and  valleys,  to 
which,  on  account  of  the  magnitude  of  the  sun,  he 
assigns  a  prodigious  extent,  some  of  the  mountains 
being  six  hundred  miles  high,  and  the  valleys  pro- 
portionally deep.  He  employs  in  his  explanation  no 
volcanic  fires,  but  supposes  two  separate  regions  of 
dense  clouds  floating  in  the  solar  atmosphere,  at  differ- 
ent distances  from  the  sun.  The  exterior  stratum  of 
clouds  he  considers  as  the  depository  of  the  sun's  light 
and  heat,  while  the  inferior  stratum  serves  as  an  awning 
or  screen  to  the  body  of  the  sun  itself,  which  thus  be- 
comes fitted  to  be  the  residence  of  animals.  The  proofs 
offered  in  support  of  this  hypothesis  are  chiefly  the  fol- 
lowing :  first,  that  the  appearances,  as  presented  to  the 
telescope,  are  such  as  accord  better  with  the  idea  that 
the  fluctuations  arise  from  the  motions  of  clouds,  than 
that  they  are  owing  to  the  agitations  of  a  liquid,  which 
could  not  depart  far  enough  from  its  general  level  to 
enable  us  to  see  its  waves  at  so  great  a  distance,  where 
a  line  forty  miles  in  length  would  subtend  an  angle  at 
the  eye  of  only  the  tenth  part  of  a  second ;  secondly, 
that,  since  clouds  are  easily  dispersed  to  any  extent,  the 
great  dimensions  which  the  solar  spots  occasionally  ex- 
hibit are  more  consistent  with  this  than  with  any  other 
hypothesis  ;  and,  finally,  that  a  lower  stratum  of  clouds, 
similar  to  those  of  our  atmosphere,  was  frequently  seen 
by  the  Doctor,  far  below  the  luminous  clouds  which  are 
the  fountains  of  light  and  heat. 

Such  are  the  views  of  one  who  had,  it  must  be  ac- 


108  LETTERS  ON  ASTRONOMY. 

knowledged,  great  powers  of  observation,  and  means 
of  observation  in  higher  perfection  than  have  ever  been 
enjoyed  by  any  other  individual ;  but,  with  all  defer- 
ence to  such  authority,  I  am  compelled  to  think  that 
the  hypothesis  is  encumbered  with  very  serious  objec- 
tions. Clouds  analogous  to  those  of  our  atmosphere 
(and  the  Doctor  expressly  asserts  that  his  lower  stratum 
of  clouds  are  analogous  to  ours,  and  reasons  respecting 
the  upper  stratum  according  to  the  same  analogy)  can- 
not exist  in  hot  air ;  they  are  tenants  only  of  cold  re- 
gions. How  can  they  be  supposed  to  exist  in  the  im- 
mediate vicinity  of  a  fire  so  intense,  that  they  are  even 
dissipated  by  it  at  the  distance  of  ninety-five  millions 
of  miles  ?  Much  less  can  they  be  supposed  to  be  the 
depositories  of  such  devouring  fire,  when  any  thing 
in  the  form  of  clouds,  floating  in  our  atmosphere,  is 
at  once  scattered  and  dissolved  by  the  accession  of 
only  a  few  degrees  of  heat.  Nothing,  moreover,  can 
be  imagined  more  unfavorable  for  radiating  heat  to  such 
a  distance,  ttuu^the  light,  inconstant  matter  of  which 
clouds  are  composed,  floating  loosely  in  the  solar  at- 
mosphere. There  is  a  logical  difficulty  in  the  case :  it 
is  ascribing  to  things  properties  which  they  are  not 
known  to  possess ;  nay,  more,  which  they  are  known 
not  to  possess.  From  variations  of  light  and  shade  in 
objects  seen  at  moderate  distances  on  the  earth,  we  are 
often  deceived  in  regard  to  their  appearances ;  and  we 
must  distrust  the  power  of  an  astronomer  to  decide 
upon  the  nature  of  matter  seen  at  the  distance  of  nine- 
ty-five millions  of  miles. 

I  think,  therefore,  we  must  confess  our  ignorance  of 
the  nature  and  constitution  of  the  sun  ;  nor  can  we,  as 
astronomers,  obtain  much  more  satisfactory  knowledge 
respecting  it  than  the  common  apprehension,  namely, 
that  it  is  an  immense  globe  of  fire.  We  have  not  yet 
learned  what  causes  are  in  operation  to  maintain  its  un- 
decaying  fires  ;  but  our  confidence  in  the  Divine  wisdom 
and  goodness  leads  us  to  believe,  that  those  causes 
are  such  as  will  preserve  those  fires  from  extinction, 
and  at  a  nearly  uniform  degree  of  intensity.  Any  ma- 


THE   SUN.  109 

terial  change  in  this  respect  would  jeopardize  the  safety 
of  the  animal  and  vegetable  kingdoms,  which  could  not 
exist  without  the  enlivening  influence  of  the  solar  heat, 
nor,  indeed,  were  that  heat  any  more  or  less  intense 
than  it  is  at  present. 

If  we,  inquire  whether  the  surface  of  the  sun  is  in  a 
state  of  actual  combustion,  like  burning  fuel,  or  merely 
in  a  state  of  intense  ignition,  like  a  stone  heated  to  red- 
ness in  a  furnace,  we  shall  find  it  most  reasonable  to 
conclude  that  it  is  in  a  state  of  ignition.  If  the  body 
of  the  sun  were  composed  of  combustible  matter  and 
were  actually  on  fire,  the  material  of  the  sun  would  be 
continually  wasting  away,  while  the  products  of  com- 
bustion would  fill  all  the  vast  surrounding  regions,  and 
obscure  the  solar  light.  But  solid  bodies  may  attain  a 
very  intense  state  of  ignition,  and  glow  with  the  most 
fervent  heat,  while  none  of  their  material  is  consumed, 
and  no  clouds  or  fumes  rise  to  obscure  their  brightness, 
or  to  impede  their  further  emission  of  heat.  An  ignited 
surface,  moreover,  is  far  better  adapted  than  flame  to  the 
radiation  of  heat.  Flame,  when  made*  to  act  in  contact 
with  the  surfaces  of  solid  bodies,  heats  them  rapidly 
and  powerfully ;  but  it  sends  forth,  or  radiates,  very 
little  heat,  compared  with  solid  matter  in  a  high  state 
of  ignition.  These  various  considerations  render  it 
highly  probable  to  my  mind,  that  the  body  of  the  sun 
is  not  in  a  state  of  actual  combustion,  but  merely  in  a 
state  of  high  ignition. 

The  solar  beam  consists  of  a  mixture  of  several  dif- 
ferent sorts  of  rays.  First,  there  are  the  calorific  rays, 
which  afford  heat,  and  are  entirely  distinct  from  those 
which  afford  light,  and  may  be  separated  from  them. 
Secondly,  there  are  the  colorific  rays,  which  give  light, 
consisting  of  rays  of  seven  distinct  colors,  namely,  vio- 
let, indigo,  blue,  green,  yellow,  orange,  red.  These, 
when  separated,  as  they  may  be  by  a  glass  prism,  com- 
pose the  prismatic  spectrum.  They  appear  also  in  the 
rainbow.  When  united  again,  in  due  proportions,  they 
constitute  white  light,  as  seen  in  the  light  of  the  sun. 

10  L.  A. 


110  LETTERS  ON  ASTRONOMY. 

Thirdly,  there  are  found  in  the  solar  beam  a  class  of 
rays  which  afford  neither  heat  nor  light,  but  which 
produce  chemical  changes  in  certain  bodies  exposed  to 
their  influence,  and  hence  are  called  chemical  rays. 
Fourthly,  there  is  still  another  class,  called  magnetiz- 
ing rays,  because  they  are  capable  of  imparting  mag- 
netic properties  to  steel.  These  different  sorts  of  rays 
are  sent  forth  from  the  sun,  to  the  remotest  regions  of 
the  planetary  worlds,  invigorating  all  things  by  their 
life-giving  influence,  and  dispelling  the  darkness  that 
naturally  fills  all  space. 

But  it  was  not  alone  to  give  heat  and  light,  that  the 
sun  was  placed  in  the  firmament.  By  his  power  of  at- 
traction, also,  he  serves  as  the  great  regulator  of  the 
planetary  motions,  bending  them  continually  from  the 
straight  line  in  which  they  tend  to  move,  and  compel- 
ling them  to  circulate  around  him,  each  at  nearly  a 
uniform  distance,  and  all  in  perfect  harmony.  I  will 
hereafter  explain  to  you  the  manner  in  which  the  grav- 
ity of  the  sun  thus  acts,  to  control  the  planetary  mo- 
tions. For  the  present,  let  us  content  ourselves  with 
reflecting  upon  the  wonderful  force  which  the  sun  must 
put  forth,  in  order  to  bend  out  of  their  courses,  into  cir- 
cular orbits,  such  a  number  of  planets,  some  of  which 
are  more  than  a  thousand  times  as  large  as  the  earth. 
Were  a  ship  of  war  under  full  sail,  and  it  should  be  re- 
quired to  turn  her  aside  from  her  course  by  a  rope  at- 
tached to  her  bow,  we  can  easily  imagine  that  it  would 
take  a  great  force  to  do  it,  especially  were  it  required 
that  the  force  should  remain  stationary  and  the  ship 
be  so  constantly  diverted  from  her  course,  as  to  be 
made  to  go  round  the  force  as  round  a  centre.  Some- 
what similar  to  this  is  the  action  which  the  sun  exerts 
on  each  of  the  planets  by  some  invisible  influence,  called 
gravitation.  The  bodies  which  he  thus  turns  out  of 
their  course,  and  bends  into  a  circular  orbit  around  him- 
self, are,  however,  many  millions  of  times  as  ponderous 
as  the  ship,  and  are  moving  many  thousand  times  as 
swiftly. 


ANNUAL  REVOLUTION.  Ill 


LETTER  XL 

ANNUAL  REVOLUTION. SEASONS. 

*'  These,  as  they  change,  Almighty  Father,  these 
Are  but  the  varied  God.    The  rolling  year 
Is  full  of  Thee." — Thomson. 

WE  have  seen  that  the  apparent  revolution  of  the 
heavenly  bodies,  from  east  to  west,  every  twenty-four 
hours,  is  owing  to  a  real  revolution  of  the  earth  on  its 
own  axis,  in  the  opposite  direction.  This  motion  is 
very  easily  understood,  resembling,  as  it  does,  the  spin- 
ning of  a  top.  We  must,  however,  conceive  of  the  top 
as  turning  without  any  visible  support,  and  not  as  rest- 
ing in  the  usual  manner  on  a  plane.  The  annual  mo- 
tion of  the  earth  around  the  sun,  which  gives  rise  to  an 
apparent  motion  of  the  sun  around  the  earth  once  a 
year,  and  occasions  the  change  of  seasons,  is  somewhat 
more  difficult  to  understand  ;  and  it  may  cost  you  some 
reflection,  before  you  will  settle  all  the  points  respect- 
ing the  changes  of  the  seasons  clearly  in  your  mind. 
We  sometimes  see  these  two  motions  exemplified  in  a 
top.  When,  as  the  string  is  pulled,  the  top  is  thrown 
forwards  on  the  floor,  we  may  see  it  move  forward 
(sometimes  in  a  circle)  at  the  same  time  that  it  spins 
on  its  axis.  Let  a  candle  be  placed  on  a  table,  to  rep- 
resent the  sun,  and  let  these  two  motions  be  imagined 
to  be  given  to  a  top  around  it,  and  we  shall  have  a  case 
somewhat  resembling  the  actual  motions  of  the  earth 
around  the  sun. 

When  bodies  are  at  such  a  distance  from  each  other 
as  the  earth  and  the  sun,  a  spectator  on  either  would 
project  the  other  body  upon  the  concave  sphere  of  the 
heavens,  always  seeing  it  on  the  opposite  side  of  a 
great  circle  one  hundred  and  eighty  degrees  from 
himself. 

Recollect  that  the  path  in  which  the  earth  move*' 


112 


LETTERS  ON  ASTRONOMY. 


round  the  sun  is  called  the  ecliptic.  We  are  not  to 
conceive  of  this,  or  of  any  other  celestial  circle,  as  hav- 
ing any  real,  palpable  existence,  any  more  than  the  path 
of  a  bird  through  the  sky.  You  will  perhaps  think  it 
quite  superfluous  for  me  to  remind  you  of  this ;  but, 
from  the  habit  of  seeing  the  orbits  of  the  heavenly  bod- 
ies represented  in  diagrams  and  orreries,  by  palpable 
lines  and  circles,  we  are  apt  inadvertently  to  acquire 
the  notion,  that  the  orbits  of  the  planets,  and  other  rep- 
resentations of  the  artificial  sphere,  have  a  real,  pal- 
pable existence  in  Nature ;  whereas,  they  denote  the 
places  where  mere  geometrical  or  imaginary  lines  run. 
You  might  have  expected  to  see  an  orrery,  exhibiting 
a  view  of  the  sun  and  planets,  with  their  various  mo- 
tions, particularly  described  in  my  Letter  on  astronom- 
ical instruments  and  apparatus.  I  must  acknowledge, 
that  I  entertain  a  very  low  opinion  of  the  utility  of  even 
the  best  orreries,  and  I  cannot  recommend  them  as 
auxiliaries  in  the  study  of  astronomy.  The  numerous 
appendages  usually  connected  with  them,  some  to  sup- 
port them  in  a  proper  position,  and  some  to  communi- 
cate to  them  the  requisite  motions,  enter  into  the  ideas 
which  the  learner  forms  respecting  the  machinery  of 
the  heavens ;  and  it  costs  much  labor  afterwards  to  di- 
vest the  mind  of  such  erroneous  impressions.  Astron- 
omy can  be  exhibited  much  more  clearly  and  beauti- 
fully to  the  mental  eye  than  to  the  visual  organ.  It  is 
much  easier  to  conceive  of  the  sun  existing  in  bound- 
less space,  and  of  the  earth  as  moving  around  him  at  a 
great  distance,  the  mind  having  nothing  in  view  but 
simply  these  two  bodies,  than  it  is,  in  an  orrery,  to  con- 
template the  motion  of  a  ball  representing  the  earth, 
carried  by  a  complicated  apparatus  of  wheels  around 
another  ball,  supported  by  a  cylinder  or  wire,  to  repre- 
sent the  sun.  I  would  advise  you,  whenever  it  is  prac- 
ticable, to  think  how  things  are  in  Nature,  rather  than 
how  they  are  represented  by  art.  The  machinery  of 
the  heavens  is  much  simpler  than  that  of  an  orrery. 
In  endeavoring  to  obtain  a  clear  idea  of  the  revolu- 


ANNUAL  REVOLUTION.  113 

tion  of  the  earth  around  the  sun,  imagine  to  yourself  a 
plane  (a  geometrical  plane,  having  merely  length  and 
breadth,  but  no  thickness)  passing  through  the  centres  of 
the  sun  and  the  earth,  and  extended  far  beyond  the  earth 
till  it  reaches  the  firmament  of  stars.  Although,  in- 
deed, no  such  dome  actually  exists  as  that  under  which 
we  figure  to  ourselves  the  vault  of  the  sky,  yet,  as  the 
fixed  stars  appear  to  be  set  in  such  a  dome,  we  may 
imagine  that  the  circles  of  the  sphere,  when  indefinite- 
ly enlarged,  finally  reach  such  an  imaginary  vault.  All 
that  is  essential  is,  that  we  should  imagine  this  to  ex- 
ist far  beyond  the  bounds  of  the  solar  system,  the  vari- 
ous bodies  that  compose  the  latter  being  situated  close 
around  the  sun,  at  the  centre. 

Along  the  line  where  this  great  circle  meets  the  star- 
ry vault,  are  situated  a  series  of  constellations, — Aries, 
Taurus,  Gemini,  &c., — which  occupy  successively  this 
portion  of  the  heavens.  When  bodies  are  at  such  a 
distance  from  each  other  as  the  sun  and  the  earth,  I 
have  said  that  a  spectator  on  either  would  project  the 
other  body  upon  the  concave  sphere  of  the  heavens, 
always  seeing  it  on  the  opposite  side  of  a  great  circle 
one  hundred  and  eighty  degrees  from  himself.  The 
place  of  a  body,  when  viewed  from  any  point,  is  denot- 
ed by  the  position  it  occupies  among  the  stars.  Thus, 
in  the  diagram,  Fig.  25,  page  114,  when  the  earth  ar- 
rives at  E,  it  is  said  to  be  in  Aries,  because,  if  viewed 
from  the  sun,  it  would  be  projected  on  that  part  of  the 
heavens ;  and,  for  the  same  reason,  to  a  spectator  at 
E,  the  sun  would  be  in  Libra.  When  the  earth  shifts 
its  position  from  Aries  to  Taurus,  as  we  are  unconscious 
of  our  own  motion,  the  sun  it  is  that  appears  to  move 
from  Libra  to  Scorpio,  in  the  opposite  part  of  the  heav- 
ens. Hence,  as  we  go  forward,  in  the  order  of  the 
signs,  on  one  side  of  the  ecliptic,  the  sun  seems  to  be 
moving  forward  at  the  same  rate  on  the  opposite  side 
of  the  same  great  circle ;  and  therefore,  although  we 
are  unconscious  of  our  own  motion,  we  can  read  it,  from 
day  to  day,  in  the  motions  of  the  sun.  If  we  could  see 
10* 


114 


LETTERS  ON  ASTRONOMY. 
Fig.  25. 


the  stars  at  the  same  time  with  the  sun,  we  could  actu- 
ally observe,  from  day  to  day,  the  sun's  progress  through 
them,  as  we  observe  the  progress  of  the  moon  at  night ; 
only  the  sun's  rate  of  motion  would  be  nearly  fourteen 
times  slower  than  that  of  the  moon.  Although  we  do 
not  see  the  stars  when  the  sun  is  present,  we  can  observe 
that  it  makes  daily  progress  eastward,  as  is  apparent 
from  the  constellations  of  the  zodiac  occupying,  succes- 
sively, the  western  sky  immediately  after  sunset,  prov- 
ing that  either  all  the  stars  have  a  common  motion 
westward,  independent  of  their  diurnal  motion,  or  that 
the  sun  has  a  motion  past  them  from  west  to  east.  We 
shall  see,  hereafter,  abundant  evidence  to  prove,  that 
this  change  in  the  relative  position  of  the  sun  and  stars, 
is  owing  to  a  change  in  the  apparent  place  of  the  sun, 
and  not  to  any  change  in  the  stars. 

To  form  a  clear  idea  of  the  two  motions  of  the  earth, 
imagine  yourself  standing  on  a  circular  platform  which 


ANNUAL  REVOLUTION.  115 

turns  slowly  round  its  centre.  While  you  are  carried 
slowly  round  the  entire  of  the  circuit  of  the  heavens, 
along  with  the  platform,  you  may  turn  round  upon  your 
heel  the  same  way  three  hundred  and  sixty-five  times. 
The  former  is  analogous  to  our  annual  motion  with  the 
earth  around  the  sun ;  the  latter,  to  our  diurnal  revolu- 
tion in  common  with  the  earth  around  its  own  axis. 

Although  the  apparent  revolution  of  the  sun  is  in  a 
direction  opposite  to  the  real  motion  of  the  earth,  as  re- 
gards absolute  space,  yet  both  are  nevertheless  from 
west  to  east,  since  these  terms  do  not  refer  to  any  di- 
rections in  absolute  space,  but  to  the  order  in  which 
certain  constellations  (the  constellations  of  the  Zodiac) 
succeed  one  another.  The  earth  itself,  on  opposite 
sides  of  its  orbit,  does  in  fact  move  towards  directly  op- 
posite points  of  space  ;  but  it  is  all  the  while  pursuing 
its  course  in  the  order  of  the  signs.  In  the  same  man- 
ner, although  the  earth  turns  on  its  axis  from  west  to 
east,  yet  any  place  on  the  surface  of  the  earth  is  moving 
in  a  direction  in  space  exactly  opposite  to  its  direction 
twelve  hours  before.  If  the  sun  left  a  visible  trace  on 
the  face  of  the  sky,  the  ecliptic  would  of  course  be  dis- 
tinctly marked  on  the  celestial  sphere,  as  it  is  on  an 
artificial  globe ;  and  were  the  equator  delineated  in  a 
similar  manner,  we  should  then  see,  at  a  glance,  the 
relative  position  of  these  two  circles, — the  points  where 
they  intersect  one  another,  constituting  the  equinoxes  ; 
the  points  where  they  are  at  the  greatest  distance  asun- 
der, that  is,  the  solstices ;  and  various  other  particu- 
lars, which,  for  want  of  such  visible  traces,  we  are  now 
obliged  to  search  for  by  indirect  and  circuitous  methods. 
It  will  aid  you,  to  have  constantly  before  your  mental 
vision  an  imaginary  delineation  of  these  two  important 
circles  on  the  face  of  the  sky. 

The  equator  makes  an  angle  with  the  ecliptic  of 
twenty-three  degrees  and  twenty-eight  minutes.  This 
is  called  the  obliquity  of  the  ecliptic.  As  the  sun  and 
earth  are  both  always  in  the  ecliptic,  and  as  the  motion 
of  the  earth  in  one  part  of  it  makes  the  sun  appear  to 


116  LETTERS  ON  ASTRONOMY. 

move  in  the  opposite  part,  at  the  same  rate,  the  sun  ap- 
parently descends,  in  Winter,  twenty-three  degrees  and 
twenty-eight  minutes  to  the  south  of  the  equator,  and 
ascends,  in  Summer,  the  same  number  of  degrees  north 
of  it.  We  must  keep  in  mind,  that  the  celestial  equa- 
tor and  celestial  ecliptic  are  here  understood,  and  we 
may  imagine  them  to  be  two  great  circles  delineated  on 
the  face  of  the  sky.  On  comparing  observations  made 
at  different  periods,  for  more  than  two  thousand  years, 
it  is  found,  that  the  obliquity  of  the  ecliptic  is  not 
constant,  but  that  it  undergoes  a  slight  diminution,  from 
age  to  age,  amounting  to  fifty-two  seconds  in  a  century, 
or  about  half  a  second  annually.  We  might  apprehend 
that,  by  successive  approaches  to  each  other,  the  equa- 
tor and  ecliptic  would  finally  coincide  ;  but  astronomers 
have  discovered,  by  a  most  profound  investigation,  based 
on  the  principles  of  universal  gravitation,  that  this  irreg- 
ularity is  confined  within  certain  narrow  limits  ;  and  that 
the  obliquity,  after  diminishing  for  some  thousands  of 
years,  will  then  increase  for  a  similar  period,  and  will 
thus  vibrate  forever  about  a  mean  value. 

As  the  earth  traverses  every  part  of  her  orbit  in  the 
course  of  a  year,  she  will  be  once  at  each  solstice,  and 
once  at  each  equinox.  The  best  way  of  obtaining  a 
correct  idea  of  her  two  motions  is,  to  conceive  of  her 
as  standing  still  for  a  single  day,  at  some  point  in  her 
orbit,  until  she  has  turned  once  on  her  axis,  then  mov- 
ing about  a  degree,  and  halting  again,  until  another 
diurnal  revolution  is  completed.  Let  us  suppose  the 
earth  at  the  Autumnal  equinox,  the  sun,  of  course,  be- 
ing at  the  Vernal  equinox, — for  we  must  always  think  of 
these  two  bodies  as  diametrically  opposite  to  each  other. 
Suppose  the  earth  to  stand  still  in  its  orbit  for  twenty- 
four  hours.  The  revolution  of  the  earth  on  its  axis, 
from  west  to  east,  will  make  the  sun  appear  to  describe 
a  great  circle  of  the  heavens  from  east  to  west,  coincid- 
ing with  the  equator.  At  the  end  of  this  period,  sup- 
pose the  sun  to  move  northward  one  degree,  and  to 
remain  there  for  twenty-four  hours  ;  in  which  time,  the 


ANNUAL  REVOLUTION.  117 


revolution  of  the  earth,  will  make  the  sun  appear  to 
describe  another  circle,  from  east  to  west,  parallel  to  the 
equator,  but  one  degree  north  of  it.  Thus,  we  may 
conceive  of  the  sun  as  moving  one  degree  north,  every 
day,  for  about  three  months,  when  it  will  reach  the  point 
of  the  ecliptic  furthest  from  the  equator,  which  point  is 
called  the  tropic,  from  a  Greek  word,  signifying  to  turn ; 
because,  after  the  sun  has  passed  this  point,  his  motion 
in  his  orbit  carries  him  continually  towards  the  equator, 
and  therefore  he  seems  to  turn  about.  The  same  point 
is  also  called  the  solstice,  from  a  Latin  word,  signify- 
ing to  stand  still ;  since,  when  the  sun  has  reached  its 
greatest  northern  or  southern  limit,  while  its  declina- 
tion is  at  the  point  where  it  ceases  to  increase,  but  be- 
gins to  decrease,  there  the  sun  seems  for  a  short  time 
stationary,  with  regard  to  the  equator,  appearing  for 
several  days  to  describe  the  same  parallel  of  latitude. 

When  the  sun  is  at  the  northern  tropic,  which  hap- 
pens about  the  twenty-first  of  June,  his  elevation  above 
the  southern  horizon  at  noon  is  the  greatest  in  the 
year ;  and  when  he  is  at  the  southern  tropic,  about  the 
twenty-first  of  December,  his  elevation  at  noon  is  the 
least  in  the  year.  The  difference  between  these  two 
meridian  altitudes  will  give  the  whole  distance  from 
one  tropic  to  the  other,  and  consequently,  twice  the  dis- 
tance from  each  tropic  to  the  equator.  By  this  means, 
we  find  how  far  the  tropic  is  from  the  equator,  and  that 
gives  us  the  angle  which  the  equator  and  ecliptic  make 
with  each  other ;  for  the  greatest  distance  between  any 
two  great  circles  on  the  sphere  is  always  equal  to  the 
angle  which  they  make  with  each  other.  Thus,  the 
ancient  astronomers  were  able  to  determine  the  obliqui- 
ty of  the  ecliptic  with  a  great  degree  of  accuracy.  It 
was  easy  to  find  the  situation  of  the  zenith,  because  the 
direction  of  a  plumb-line  shows  us  where  that  is ;  and 
it  was  easy  to  find  the  distances  from  the  zenith  where 
the  sun  was  at  the  greatest  and  least  distances,  respec- 
tively. The  difference  of  these  two  arcs  is  the  angu- 
lar distance  from  one  tropic  to  the  other ;  and  half  this 


118  LETTERS  ON  ASTRONOMY. 

arc  is  the  distance  of  either  tropic  from  the  equator, 
and  of  course,  equal  to  the  obliquity  of  the  ecliptic. 
All  this  will  be  very  easily  understood  from  the  annexed 
diagram,  Fig.  26.  Let  Z  be 
the  zenith  of  a  spectator  sit- 
uated at  C ;  Z  n  the  least, 
and  Z  s  the  greatest  distance 
of  the  sun  from  the  zenith. 
From  Z  s  subtract  Z  n,  and 
then  s  n,  the  difference,  di- 
vided by  two,  will  give  the 
obliquity  of  the  ecliptic. 

The  motion  of  the  earth 
in  its  orbit  is  nearly  seventy 
times  as  great  as  its  greatest 
motion  around  its  axis.  In  its  revolution  around  the 
sun,  the  earth  moves  no  less  than  one  million  six  hun- 
dred and  forty  thousand  miles  per  day,  sixty-eight  thous- 
and miles  per  hour,  eleven  hundred  miles  per  minute, 
and  nearly  nineteen  miles  every  second ;  a  velocity  near- 
ly sixty  times  as  great  as  the  greatest  velocity  of  a  can- 
non ball.  Places  on  the  earth  turn  with  very  different 
degrees  of  velocity  in  different  latitudes.  Those  near 
the  equator  are  carried  round  on  the  circumference  of 
a  large  circle ;  those  towards  the  poles,  on  the  circum- 
ference of  a  small  circle ;  while  one  standing  on  the 
pole  itself  would  not  turn  at  all.  Those  who  live  on 
the  equator  are  carried  about  one  thousand  miles  an 
hour.  In  our  latitude,  (forty-one  degrees  and  eighteen 
minutes,)  the  diurnal  velocity  is  about  seven  hundred 
and  fifty  miles  per  hour.  It  would  seem,  at  first  view, 
quite  incredible,  that  we  should  be  whirled  round  at  so 
rapid  a  rate,  and  yet  be  entirely  insensible  of  any  mo- 
tion ;  and  much  more,  that  we  could  be  going  so  swiftly 
through  space,  in  our  circuit  around  the  sun,  while  all 
things,  when  unaffected  by  local  causes,  appear  to  be 
in  such  a  state  of  quiescence.  Yet  we  have  the  most 
unquestionable  evidence  of  the  fact ;  nor  is  it  difficult 
to  account  for  it,  in  consistency  with  the  general  state 


SEASONS.  119 

of  repose  among  bodies  on  the  earth,  when  we  reflect 
that  their  relative  motions,  with  respect  to  each  other, 
are  not  in  the  least  disturbed  by  any  motions  which 
they  may  have  in  common.  When  we  are  on  board  a 
steam-boat,  we  move  about  in  the  same  manner  when 
the  boat  is  in  rapid  motion,  as  when  it  is  lying  still ; 
and  such  would  be  the  case,  if  it  moved  steadily  a  hun- 
dred times  faster  than  it  does.  -Were  the  earth,  how- 
ever, suddenly  to  stop  its  diurnal  revolution,  all  movable 
bodies  on  its  surface  would  be  thrown  off  in  tangents 
to  the  surface  with  velocities  proportional  to  that  of  their 
diurnal  motion  ;  and  were  the  earth  suddenly  to  halt  in 
its  orbit,  we  should  be  hurled  forward  into  space  with 
inconceivable  rapidity. 

I  will  next  endeavor  to  explain  to  you  the  phenom- 
ena of  the  Seasons.  These  depend  on  two  causes; 
first,  the  inclination  of  the  earth's  axis  to  the  plane  of 
its  orbit ;  and,  secondly,  to  the  circumstance,  that  the 
axis  always  remains  parallel  to  itself.  Imagine  to  your- 
self a  candle  placed  in  the  centre  of  a  ring,  to  represent 
the  sun  in  the  centre  of  the  earth's  orbit,  and  an  apple 
with  a  knittingneedle  running  through  it  in  the  direc- 
tion of  the  stem.  Run  a  knife  around  the  central  part 
of  the  apple,  to  mark  the  situation  of  the  equator.  The 
circumference  of  the  ring  represents  the  earth's  orbit 
in  the  plane  of  the  ecliptic.  Place  the  apple  so  that 
the  equator  shall  coincide  with  the  wire ;  then  the  axis 
will  lie  directly  across  the  plane  of  the  ecliptic  ;  that  is, 
at  right  angles  to  it.  Let  the  apple  be  carried  quite 
round  the  ring,  constantly  preserving  the  axis  parallel 
to  itself,  and  the  equator  all  the  while  coinciding  with 
the  wire  that  represents  the  orbit.  Now,  since  the  sun 
enlightens  half  the  globe  at  once,  so  the  candle,  which 
here  represents  the  sun,  will  shine  on  the  half  of  the 
apple  that  is  turned  towards  it ;  and  the  circle  which 
divides  the  enlightened  from  the  unenlightened  side  of 
the  apple,  called  the  terminator,  will  pass  through  both 
the  poles.  If  the  apple  be  turned  slowly  round  on  its 
axis,  the  terminator  will  successively  pass  over  all  places 


120  LETTERS  ON  ASTRONOMY. 

on  the  earth,  giving  the  appearance  of  sunrise  to  places 
at  which  it  arrives,  and  of  sunset  to  places  from  which 
it  departs.  If,  therefore,  the  equator  had  coincided  with 
the  ecliptic,  as  would  have  been  the  case,  had  the  earth's 
axis  been  perpendicular  to  the  plane  of  its  orbit,  the 
diurnal  motion  of  the  sun  would  always  have  been  in 
the  equator,  and  the  days  and  nights  would  have  been 
equal  all  over  the  globe.  To  the  inhabitants  of  the 
equatorial  parts  of  the  earth,  the  sun  would  always  have 
appeared  to  move  in  the  prime  vertical,  rising  directly 
in  the  east,  passing  through  the  zenith  at  noon,  and 
setting  in  the  west.  In  the  polar  regions,  the  sun  would 
always  have  appeared  to  revolve  in  the  horizon  ;  while, 
at  any  place  between  the  equator  and  the  pole,  the 
course  of  the  sun  would  have  been  oblique  to  the  hori- 
zon, but  always  oblique  in  the  same  degree.  There 
would  have  been  nothing  of  those  agreeable  vicissitudes 
of  the  seasons  which  we  now  enjoy ;  but  some  regions 
of  the  earth  would  have  been  crowned  with  perpetual 
spring,  others  would  have  been  scorched  with  the  unre- 
mitting, fervor  of  a  vertical  sun,  while  extensive  regions 
towards  either  pole  would  have  been  consigned  to  ever- 
lasting frost  and  sterility. 

To  understand,  then,  clearly,  the  causes  of  the  change 
of  seasons,  use  the  same  apparatus  as  before ;  but,  in- 
stead of  placing  the  axis  of  the  earth  at  right  angles  to 
the  plane  of  its  orbit,  turn  it  out  of  a  perpendicular  po- 
sition a  little,  (twenty-three  degrees  and  twenty-eight 
minutes,)  then  the  equator  will  be  turned  just  the  same 
number  of  degrees  out  of  a  coincidence  with  the  ecliptic. 
Let  the  apple  be  carried  around  the  ring,  always  hold- 
ing the  axis  inclined  at  the  same  angle  to  the  plane  of 
the  ring,  and  always  parallel  to  itself.  You  will  find 
that  there  will  be  two  points  in  the  circuit  where  the 
plane  of  the  equator,  that  you  had  marked  around  the 
centre  of  the  apple,  will  pass  through  the  centre  of  the 
sun ;  these  will  be  the  points  where  the  celestial  equa- 
tor and  the  ecliptic  cut  one  another,  or  the  equinoxes. 
When  the  earth  is  at  either  of  these  points,  the  sun 


SEASONS.  121 

shines  on  both  poles  alike ;  and,  if  we  conceive  of  the 
earth,  while  in  this  situation,  as  turning  once  round  on 
its  axis,  the  apparent  diurnal  motion  of  the  sun  will  be 
the  same  as  it  would  be,  were  the  earth's  axis  perpen- 
dicular to  the  plane  of  the  equator.  For  that  day,  the 
sun  would  revolve  in  the  equator,  and  the  days  and 
nights  would  be  equal  all  over  the  globe.  If  the  apple 
were  carried  round  in  the  manner  supposed,  then,  at 
the  distance  of  ninety  degrees  from  the  equinoxes,  the 
same  pole  would  be  turned  from  the  sun  on  one  side, 
just  as  much  as  it  was  turned  towards  him  on  the  other. 
In  the  former  case,  the  sun's  light  would  fall  short  of  the 
pole  twenty-three  and  one  half  degrees,  and  in  the  other 
case,  it  would  reach  beyond  it  the  same  number  of  de- 
grees. I  would  recommend  to  you  to  obtain  as  clear 
an  idea  as  you  can  of  the  cause  of  the  change  of  sea- 
sons, by  thinking  over  the  foregoing  illustration.  You 
may  then  clear  up  any  remaining  difficulties,  by  study- 
ing the  diagram,  Fig.  27,  on  page  122. 

Let  A  B  C  D  represent  the  earth's  place  in  different 
parts  of  its  orbit,  having  the  sun  in  the  centre.     Let 

A,  C,  be  the  positions  of  the  earth  at  the  equinoxes,  and 

B,  D,  its  positions  at  the  tropics, — the  axis  n  s  being  al- 
ways parallel  to  itself.     It  is  difficult  to  represent  things 
of  this  kind  correctly,  all  on  the  same  plane ;  but  you 
will  readily  see,  that  the  figure  of  the  earth,  here,  an- 
swers to  the  apple  in  the  former  illustration ;  that  the 
hemisphere  towards  n  is  above,  and  that  towards  s  is 
below,  the  plane  of  the  paper.     When  the  earth  is  at 
A  and  C,  the  Vernal  and  Autumnal  equinoxes,  the  sun, 
you  will  perceive,  shines  on  both  the  poles  n  and  s ;  and, 
if  you  conceive  of  the  globe,  while  in  this  position,  as 
turned  round  on  its  axis,  as  it  is  in  the  diurnal  revolu- 
tion, you  will  readily  understand,  that  the  sun  would 
describe  the  celestial  equator.     This  may  not  at  first 
appear  so  obvious,  by  inspecting  the  figure ;  but  if  you 
consider  the  point  n  as  raised  above  the  plane  of  the 
paper,  and  the  point  s  as  depressed  below  it,  you  will 
readily  see  how  the  plane  of  the  equator  would  pass 

11  L.  A. 


122 


LETTERS  ON  ASTRONOMY. 
Fig.  27. 


"Tft 


through  the  centre  of  the  sun.  Again,  at  B,  when  the 
earth  is  at  the  southern  tropic,  the  sun  shines  twenty- 
three  and  a  half  degrees  beyond  the  north  pole,  n,  and 
falls  the  same  distance  short  of  the  south  pole,  s.  The 
case  is  exactly  reversed  when  the  earth  is  at  the  north- 
ern tropic,  and  the  sun  at  the  southern.  While  the 
earth  is  at  one  of  the  tropics,  at  B,  for  example,  let  us 
conceive  of  it  as  turning  on  its  axis,  and  we  shall  read- 
ily see,  that  all  that  part  of  the  earth  which  lies  within 
the  north  polar  circle  will  enjoy  continual  day,  while 
that  within  the  south  polar  circle  will  have  continual 
night ;  and  that  all  other  places  will  have  their  days 
longer  as  they  are  nearer  to  the  enlightened  pole,  and 
shorter  as  they  are  nearer  to  the  unenlightened  pole. 


SEASONS.  123 

This  figure  likewise  shows  the  successive  positions  of 
the  earth,  at  different  periods  of  the  year,  with  respect 
to  the  signs,  and  what  months  correspond  to  particular 
signs.  Thus,  the  earth  enters  Libra,  and  the  sun  Aries, 
on  the  twenty-first  of  March,  and  on  the  twenty-first 
of  June,  the  earth  is  just  entering  Capricorn,  and  the 
sun,  Cancer.  You  will  call  to  mind  what  is  meant 
by  this  phraseology, — that  by  saying  the  earth  enters 
Libra,  we  mean  that  a  spectator  placed  on  the  sun 
would  see  the  earth  in  that  part  of  the  celestial  ecliptic, 
which  is  occupied  by  the  sign  Libra ;  and  that  a  spec- 
tator on  the  earth  sees  the  sun  at  the  same  time  pro- 
jected on  the  opposite  part  of  the  heavens,  occupied  by 
the  sign  Cancer. 

Had  the  axis  of  the  earth  been  perpendicular  to  the 
plane  of  the  ecliptic,  then  the  sun  would  always  have 
appeared  to  move  in  the  equator,  the  days  would  every 
where  have  been  equal  to  the  nightsx  and  there  could 
have  been  no  change  of  seasons.  On  the  other  hand, 
had  the  inclination  of  the  ecliptic  to  the  equator  been 
much  greater  than  it  is,  the  vicissitudes  of  the  seasons 
would  have  been  proportionally  greater,  than  at  present. 
Suppose,  for  instance,  the  equator  had  been  at  right 
angles  to  the  ecliptic,  in  which  case,  the  poles  of  the 
earth  would  have  been  situated  in  the  ecliptic  itself; 
then,  in  different  parts  of  the  earth,  the  appearances 
would  have  been  as  follows :  To  a  spectator  on  the 
equator,  (where  all  the  circles  of  diurnal  revolution  are 
perpendicular  to  the  horizon,)  the  sun,  as  he  left  the 
vernal  equinox,  would  every  day  perform  his  diurnal 
revolution  in  a  smaller  and  smaller  circle,  until  he  reach- 
ed the  north  pole,  when  he  would  halt  for  a  moment, 
and  then  wheel  about  and  return  to  the  equator,  in  a 
reverse  order.  The  progress  of  the  sun  through  the 
southern  signs,  to  the  south  pole,  would  be  similar  to 
that  already  described.  Such  would  be  the  appear- 
ances to  an  inhabitant  of  the  equatorial  regions.  To  a 
spectator  living  in  an  oblique  sphere,  in  our  own  lati- 
tude, for  example,  the  sun,  while  north  of  the  equator, 


124  LETTERS   ON  ASTRONOMY. 

would  advance  continually  northward,  making  his  diur- 
nal circuit  in  parallels  further  and  further  distant  from 
the  equator,  until  he  reached  the  circle  of  perpetual 
apparition ;  after  which,  he  would  climb,  by  a  spiral 
course,  to  the  north  star,  and  then  as  rapidly  return  to 
the  equator.  By  a  similar  progress  southward,  the  sun 
would  at  length  pass  the  circle  of  perpetual  occultation, 
and  for  some  time  (which  would  be  longer  or  shorter, 
according  to  the  latitude  of  the  place  of  observation) 
there  would  be  continual  night.  To  a  spectator  on  the 
pole  of  the  earth  and  under  the  pole  of  the  heaven, 
during  the  long  day  of  six  months,  the  sun  would  wind 
its  way  to  a  point  directly  over  head,  pouring  down 
upon  the  earth  beneath  not  merely  the  heat  of  the  tor- 
rid zone,  but  the  heat  of  a  torrid  noon,  accumulating 
without  intermission. 

The  great  vicissitudes  of  heat  and  cold,  which  would 
attend  these  several  movements  of  the  sun,  would  be 
wholly  incompatible  with  the  existence  of  either  the 
animal  or  the  vegetable  kingdom,  and  all  terrestria1  Na- 
ture would  be  doomed  to  perpetual  sterility  and  deso- 
lation. The  happy  provision  which  the  Creator  has 
made  against  such  extreme  vicissitudes,  by  confining 
the  changes  of  the  seasons  within  such  narrow  bounds, 
conspires  with  many  other  express  arrangements  in  the 
economy  of  Nature,  to  secure  the  safety  and  comfort 
of  the  human  race. 

Perhaps  you  have  never  reflected  upon  all  the  rea- 
sons, why  the  several  changes  of  position,  with  respect 
to  the  horizon,  which  the  sun  undergoes  in  the  course 
of  the  year,  occasion  such  a  difference  in  the  amount 
of  heat  received  from  him.  Two  causes  contribute  to 
increase  the  heat  of  Summer  and  the  cold  of  Winter. 
The  higher  the  sun  ascends  above  the  horizon,  the  more 
directly  his  rays  fall  upon  the  earth ;  and  their  heating 
power  is  rapidly  augmented,  as  they  approach  a  per- 
pendicular direction.  When  the  sun  is  nearly  over 
head,  his  rays  strike  us  with  far  greater  force  than  when 
they  meet  us  obliquely ;  and  the  earth  absorbs  a  far 


SEASONS.  125 

greater  number  of  those  rays  of  heat  which  strike  it 
perpendicularly,  than  of  those  which  meet  it  in  a  slant- 
ing direction.  When  the  sun  is  near  the  horizon,  his 
rays  merely  glance  along  the  ground,  and  many  of  them, 
before  they  reach  it,  are  absorbed  and  dispersed  in  pass- 
ing through  the  atmosphere.  Those  who  have  felt  only 
the  oblique  solar  rays,  as  they  fall  upon  objects  in  the 
high  latitudes,  have  a  very  inadequate  idea  of  the  pow- 
er of  a  vertical,  noonday  sun,  as  felt  in  the  region  of 
the  equator. 

The  increased  length  of  the  day  in  Summer  is  anoth- 
er cause  of  the  heat  of  this  season  of  the  year.  This 
cause  more  sensibly  affects  places  far  removed  from  the 
equator,  because  at  such  places  the  days  are  longer 
and  the  nights  shorter  than  in  the  torrid  zone.  By  the 
operation  of  this  cause,  the  solar  heat  accumulates  there 
so  much,  during  the  longest  days  of  Summer,  that  the 
temperature  rises  to  a  higher  degree  than  is  often  known 
in  the  torrid  climates. 

EJrt  the  temperature  of  a  place  is  influenced  very 
much  by  several  other  causes,  as  well  as  by  the  force 
and  duration  of  the  sun's  heat.  First,  the  elevation  of 
a  country  above  the  level  of  the  sea  has  a  great  influ- 
ence upon  its  climate.  Elevated  districts  of  country, 
even  in  the  torrid  zone,  often  enjoy  the  most  agreeable 
climate  in  the  world.  The  cold  of  the  upper  regions 
of  the  atmosphere  modifies  and  tempers  the  solar  heat, 
so  as  to  give  a  most  delightful  softness,  while  the  uni- 
formity of  temperature  excludes  those  sudden  and  ex- 
cessive changes  which  are  often  experienced  in  less 
favored  climes.  In  ascending  certain  high  mountains 
situated  within  the  torrid  zone,  the  traveller  passes,  in 
a  short  time,  through  every  variety  of  climate,  from  the 
most  oppressive  and  sultry  heat,  to  the  soft  and  balmy 
air  of  Spring,  which  again  is  succeeded  by  the  cooler 
breezes  of  Autumn,  and  then  by  the  severest  frosts  of 
Winter.  A  corresponding  difference  is  seen  in  the 
products  of  the  vegetable  kingdom.  While  Winter 
reigns  on  the  summit  of  the  mountain,  its  central  re- 
11* 


126  LETTERS  ON  ASTRONOMY. 

gions  may  be  encircled  with  the  verdure  of  Spring,  and 
its  base  with  the  flowers  and  fruits  of  Summer.  Sec- 
ondly, the  proximity  of  the  ocean  also  has  a  great  effect 
to  equalize  the  temperature  of  a  place.  As  the  ocean 
changes  its  temperature  during  the  year  much  less  than 
the  land,  it  becomes  a  source  of  warmth  to  contiguous 
countries  in  Winter,  and  a  fountain  of  cool  breezes  in 
Summer.  Thirdly,  the  relative  humidity  or  dryness 
of  the  atmosphere  of  a  place  is  of  great  importance,  in 
regard  to  its  effects  on  the  animal  system.  A  dry  air 
of  ninety  degrees  is  not  so  insupportable  as  a  humid  air 
of  eighty  degrees ;  and  it  may  be  asserted  as  a  general 
principle,  that  a  hot  and  humid  atmosphere  is  unhealthy, 
although  a  hot  air,  when  dry,  may  be  very  salubrious. 
In  a  warm  atmosphere  which  is  dry,  the  evaporation 
of  moisture  from  the  surface  of  the  body  is  rapid,  and 
its  cooling  influence  affords  a  most  striking  relief  to  an 
intense  heat  without ;  but  when  the  surrounding  atmos- 
phere is  already  filled  with  moisture,  no  such  evapora- 
tion takes  place  from  the  surface  of  the  skin,  and  no 
such  refreshing  effects  are  experienced  from  this  cause. 
Moisture  collects  on  the  skin ;  a  sultry,  oppressive  sen- 
sation is  felt ;  and  chills  and  fevers  are  usually  in  the 
train. 


LETTER  XII. 


LAWS    OF   MOTION. 


;  What  though  in  solemn  silence,  all 

Move  round  this  dark,  terrestrial  ball ! 

In  reason's  ear  they  all  rejoice, 

And  utter  forth  a  glorious  voice ; 

For  ever  singing,  as  they  shine, 
'  The  hand  that  made  us  is  divine.'  " — Addison. 


HOWEVER  incredible  it  may  seem,  no  fact  is  more 
certain,  than  that  the  earth  is  constantly  on  the  wing, 
flying  around  the  sun  with  a  velocity  so  prodigious,  that, 
for  every  breath  we  draw,  we  advance  on  our  way  forty 


LAWS  OF  MOTION.  127 

or  fifty  miles.  If,  when  passing  across  the  waters  in 
a  steam-boat,  we  can  wake,  after  a  night's  repose, 
and  find  ourselves  conducted  on  our  voyage  a  hundred 
miles,  we  exult  in  the  triumphs  of  art,  which  could  have 
moved  so  ponderous  a  body  as  a  steam-ship  over  such 
a  space  in  so  short  a  time,  and  so  quietly,  too,  as  not  to 
disturb  our  slumbers ;  but,  with  a  motion  vastly  more 
quiet  and  uniform,  we  have,  in  the  same  interval,  been 
carried  along  with  the  earth  in  its  orbit  more  than  half 
a  million  of  miles.  In  the  case  of  the  steam-ship,  how- 
ever perfect  the  machinery  may  be,  we  still,  in  our 
waking  hours  at  least,  are  made  sensible  of  the  action 
of  the  forces  by  which  the  motion  is  maintained, — as 
the  roaring  of  the  fire,  the  beating  of  the  piston,  and 
the  dashing  of  the  paddle-wheels ;  but  in  the  more 
perfect  machinery  which  carries  the  earth  forward  on 
her  grander  voyage,  no  sound  is  heard,  nor  the  least  in- 
timation afforded  of  the  stupendous  forces  by  which  this 
motion  is  achieved.  To  the  pious  observer  of  Nature 
it  might  seem  sufficient,  without  any  inquiry  into  sec- 
ond causes,  to  ascribe  the  motions  of  the  spheres  to  the 
direct  agency  of  the  Supreme  Being.  If,  however,  we 
can  succeed  in  finding  the  secret  springs  and  cords,  by 
which  the  motions  of  the  heavenly  bodies  are  immedi- 
ately produced  and  controlled,  it  will  detract  nothing 
from  our  just  admiration  of  the  Great  First  Cause  of  all 
things.  We  may  therefore  now  enter  upon  the  inquiry 
into  the  nature  or  laws  of  the  forces  by  which  the  earth 
is  made  to  revolve  on  her  axis  and  in  her  orbit ;  and 
having  learned  what  it  is,  that  causes  and  maintains  the 
motions  of  the  earth,  you  will  then  acquire,  at  the  same 
time,  a  knowledge  of  all  the  celestial  machinery.  The 
subject  will  involve  an  explanation  of  the  laws  of  mo- 
tion, and  of  th£  principles  of  universal  gravitation. 

It  was  once?  supposed,  that  we  could  never  reason  re- 
specting the  laws  that  govern  the  heavenly  bodies  from 
what  we  observe  in  bodies  around  us,  but  that  motion 
is  one  thing  on  the  earth  and  quite  another  thing  in  the 
skies ;  and  hence,  that  it  is  impossible  for  us,  by  any 


128  LETTERS  ON  ASTRONOMY. 

inquiries  into  the  laws  of  terrestrial  Nature,  to  ascertain 
how  things  take  place  among  the  heavenly  bodies. 
Galileo  and  Newton,  however,  proceeded  on  the  con- 
trary supposition,  that  Nature  is  uniform  in  all  her 
works  ;  that  the  same  Almighty  arm  rules  over  all ;  and 
that  He  works  by  the  same  fixed  laws  through  all  parts 
of  His  boundless  realm.  The  certainty  with  which  all 
the  predictions  of  astronomers,  made  on  these  supposi- 
tions, are  fulfilled,  attest  the  soundness  of  the  hypoth- 
esis. Accordingly,  those  laws,  which  all  experience, 
endlessly  multiplied  and  varied,  proves  to  be  the  laws 
of  terrestrial  motion,  are  held  to  be  the  laws  that  gov- 
ern also  the  motions  of  the  most  distant  planets  and 
stars,  and  to  prevail  throughout  the  universe  of  matter. 
Let  us,  then,  briefly  review  these  great  laws  of  motion, 
which  are  three  in  number.  The  FIRST  LAW  is  as  fol- 
lows :  every  body  perseveres  in  a  state  of  rest,  or  of 
uniform  motion  in  a  straight  line,  unless  compelled 
by  some  force  to  change  its  state.  By  force  is  meant 
any  thing  which  produces  motion. 

The  foregoing  law  has  been  fully  established  by  ex- 
periment, and  is  conformable  to  all  experience.  It  em- 
braces several  particulars.  First,  a  body,  when  at  rest, 
remains  so,  unless  some  force  puts  it  in  motion ;  and 
hence  it  is  inferred,  when  a  body  is  found  in  motion, 
that  some  force  must  have  been  applied  to  it  sufficient 
to  have  caused  its  motion.  Thus,  the  fact,  that  the 
earth  is  in  motion  around  the  sun  and  around  its  own 
axis,  is  to  be  accounted  for  by  assigning  to  each  of 
these  motions  a  force  adequate,  both  in  quantity  and 
direction,  to  produce  these  motions,  respectively. 

Secondly,  when  a  body  is  once  in  motion,  it  will 
continue  to  move  for  ever,  unless  something  stops  it. 
When  a  ball  is  struck  on  the  surface  of  the  earth,  the 
friction  of  the  earth  and  the  resistance  of  the  air  soon 
stop  its  motion ;  when  struck  on  smooth  ice,  it  will 
go  much  further  before  it  comes  to  a  state  of  rest,  be- 
cause the  ice  opposes  much  less  resistance  than  the 
ground ;  and,  were  there  no  impediment  to  its  motion. 


LAWS  OF  MOTION.  129 

it  would,  when  once  set  in  motion,  continue  to  move 
without  end.  The  heavenly  bodies  are  actually  in  this 
condition  :  they  continue  to  move,  not  because  any  new 
forces  are  applied  to  them ;  but,  having  been  once  set 
in  motion,  they  continue  in  motion  because  there  is 
nothing  to  stop  them.  This  property  in  bodies  to  per- 
severe in  the  state  they  are  actually  in, — if  at  rest,  to 
remain  at  rest,  or,  if  in  motion,  to  continue  in  mo- 
tion,— is  called  inertia.  The  inertia  of  a  body  (which 
is  measured  by  the  force  required  to  overcome  it)  is 
proportioned  to  the  quantity  of  matter  it  contains.  A 
steam-boat  manifests  its  inertia,  on  first  starting  it,  by 
the  enormous  expenditure  of  force  required  to  bring  it 
to  a  given  rate  of  motion ;  and  it  again  manifests  its 
inertia,  when  in  rapid  motion,  by  the  great  difficulty  of 
stopping  it.  The  heavenly  bodies,  having  been  once 
put  in  motion,  and  meeting  with  nothing  to  stop  them, 
move  on  by  their  own  inertia.  A  top  affords  a  beauti- 
ful illustration  of  inertia,  continuing,  as  it  does,  to  spin 
after  the  moving  force  is  withdrawn. 

Thirdly,  the  motion  to  which  a  body  naturally  tends 
is  uniform ;  that  is,  the  body  moves  just  as  far  the  sec- 
ond minute  as  it  did  the  first,  and  as  far  the  third  as  the 
second ;  and  passes  over  equal  spaces  in  equal  times. 
I  do  not  assert  that  the  motion  of  all  moving  bodies  is 
in  fact  uniform,  but  that  such  is  their  tendency.  If  it 
is  otherwise  than  uniform,  there  is  some  cause  operating 
to  disturb  the  uniformity  to  which  it  is  naturally  prone. 

Fourthly,  a  body  in  motion  will  move  in  a  straight 
lim,  unless  diverted  out  of  that  line  by  some  external 
force ;  and  the  body  will  resume  its  straight-forward 
motion,  whenever  the  force  that  turns  it  aside  is  with- 
drawn. Every  body  that  is  revolving  in  an  orbit,  like 
the  moon  around  the  earth,  or  the  earth  around  the 
sun,  tends  to  move  in  a  straight  line  which  is  a  tangent* 
to  its  orbit.  Thus,  if  A  B  C,  Fig.  28,  represents  the 
orbit  of  the  moon  around  the  earth,  were  it  not  for  the 

*  A  tangent  is  a  straight  line  touching  a  circle,  as  A  D,  in  Fig.  28. 


130  LETTERS  ON  ASTRONOMY. 


constant  action  of  some  force  that  draws  her  towards 
the  earth,  she  would  move  off  in  a  straight  line.  If  the 
force  that  carries  her  towards  the  earth  were  suspended 
at  A,  she  would  immediately  desert  the  circular  motion, 
and  proceed  in  the  direction  AD.  In  the  same  man- 
ner, a  boy  whirls  a  stone  around  his  head  in  a  sling, 
and  then  letting  go  one  of  the  strings,  and  releasing  the 
force  that  binds  it  to  the  circle,  it  flies  off  in  a  straight 
line  which  is  a  tangent  to  that  part  of  the  circle  where 
it  was  released.  This  tendency  which  a  body  revolving 
in  an  orbit  exhibits,  to  recede  from  the  centre  and  to  fly 
ofT  in  a  tangent,  is  called  the  centrifugal  force.  We 
see  it  manifested  when  a  pail  of  water  is  whirled.  The 
water  rises  on  the  sides  of  the  vessel,  leaving  a  hollow 
in  the  central  parts.  We  see  an  example  of  the  effects 
of  centrifugal  action,  when  a  horse  turns  swiftly  round 
a  corner,  and  the  rider  is  thrown  outwards ;  also,  when 
a  wheel  passes  rapidly  through  a  small  collection  of 
water,  and  portions  of  the  water  are  thrown  off  from 
the  top  of  the  wheel  in  straight  lines  which  are  tangents 
to  the  wheel. 

The  centrifugal  force  is  increased  as  the  velocity  is 
increased.  Thus,  the  parts  of  a  millstone  most  remote 
from  the  centre  sometimes  acquire  a  centrifugal  force 


LAWS  OF  MOTION.  131 

so  much  greater  than  the  central  parts,  which  move 
much  slower,  that  the  stone  is  divided,  and  the  exterior 
portions  are  projected  with  great  violence.  In  like 
manner,  as  the  equatorial  parts  of  the  earth,  in  the 
diurnal  revolution,  revolve  much  faster  than  the  parts 
towards  the  poles,  so  the  centrifugal  force  is  felt  most 
at  the  equator,  and  becomes  strikingly  manifest  by  the 
diminished  weight  of  bodies,  since  it  acts  in  opposition 
to  the  force  of  gravity. 

Although  the  foregoing  law  of  motion,  when  first 
presented  to  the  mind,  appears  to  convey  no  new  truth, 
but  only  to  enunciate  in  a  formal  manner  what  we 
knew  before  ;  yet  a  just  understanding  of  this  law,  in  all 
its  bearings,  leads  us  to  a  clear  comprehension  of  no 
small  share  of  all  the  phenomena  of  motion.  The 
second  and  third  laws  may  be  explained  in  fewer  terms. 

The  SECOND  LAW  of  motion  is  as  follows :  motion  is 
proportioned  to  the  force  impressed,  and  in  the  direc- 
tion of  that  force. 

The  meaning  of  this  law  is,  that  every  force  that  is 
applied  to  a  body  produces  its  full  effect,  proportioned 
to  its  intensity,  either  in  causing  or  in  preventing  mo- 
tion. Let  there  be  ever  so  many  blows  applied  at  once 
to  a  ball,  each  will  produce  its  own  effect  in  its  own 
direction,  and  the  ball  will  move  off,  not  indeed  in  the 
zigzag,  complex  lines  corresponding  to  the  directions 
of  the  several  forces,  but  in  a  single  line  expressing 
the  united  effect  of  all.  If  you  place  a  ball  at  the  cor- 
ner of  a  table,  and  give  it  an  impulse,  at  the  same  in- 
stant, with  the  thumb  and  finger  of  each  hand,  one  im- 
pelling it  in  the  direction  of  one  side  of  the  table,  and 
the  other  in  the  direction  of  the  other  side,  the  ball  will 
move  diagonally  across  the  table.  If  the  blows  be  ex- 
actly proportioned  each  to  the  length  of  the  side  of  the 
table  on  which  it  is  directed,  the  ball  will  run  exactly 
from  corner  to  corner,  and  in  the  same  time  that  it 
would  have  passed  over  each  side  by  the  blow  given  in 
the  direction  of  that  side.  This  principle  is  expressed 
by  saying,  that  a  body  impelled  by  two  forces,  acting 


132  LETTERS  ON  ASTRONOMY. 

respectively  in  the  directions  of  the  two  sides  of  a  par- 
allelogram, and  proportioned  in  intensity  to  the  lengths 
of  the  sides,  will  describe  the  diagonal  of  the  parallelo- 
gram in  the  same  time  in  which  it  would  have  described 
the  sides  by  the  forces  acting  separately. 

The  converse  of  this  proposition  is  also  true,  namely, 
that  any  single  motion  may  be  considered  as  the  result- 
ant of  two  others, — the  motion  itself  being  represented 
by  the  diagonal,  while  the  two  components  are  repre- 
sented by  the  sides,  of  a  parallelogram.  This  reduction 
of  a  motion  to  the  individual  motions  that  produce  it, 
is  called  the  resolution  of  motion,  or  the  resolution  of 
forces.  Nor  can  a  given  motion  be  resolved  into  two 
components,  merely.  These,  again,  may  be  resolved 
into  others,  varying  indefinitely,  in  direction  and  inten- 
sity, from  all  which  the  given  motion  may  be  considered 
as  having  resulted.  This  composition  and  resolution 
of  motion  or  forces  is  often  of  great  use,  in  inquiries 
into  the  motions  of  the  heavenly  bodies.  The  compo- 
sition often  enables  us  to  substitute  a  single  force  for 
a  great  number  of  others,  whose  individual  operations 
would  be  too  complicated  to  be  followed.  By  this 
means,  the  investigation  is  greatly  simplified.  On  the 
other  hand,  it  is  frequently  very  convenient  to  resolve 
a  given  motion  into  two  or  more  others,  some  of  which 
may  be  thrown  out  of  the  account,  as  not  influencing 
the  particular  point  which  we  are  inquiring  about,  while 
others  are  far  more  easily  understood  and  managed  than 
the  single  force  would  have  been.  It  is  characteristic 
of  great  minds,  to  simplify  these  inquiries.  They  gain 
an  insight  into  complicated  and  difficult  subjects,  not 
so  much  by  any  extraordinary  faculty  of  seeing  in  the 
dark,  as  by  the  power  of  removing  from  the  object  all 
incidental  causes  of  obscurity,  until  it  shines  in  its  own 
clear  and  simple  light. 

If  every  force,  when  applied  to  a  body,  produces  its 
full  and  legitimate  effect,  how  many  other  forces  soever 
may  act  upon  it,  impelling  it  different  ways,  then  it 
must  follow,  that  the  smallest  force  ought  to  move  the 


LAWS  OF  MOTION.  133 


largest  body  ;  and  such  is  in  fact  the  case.  A  snap  of 
a  finger  upon  a  seventy-four  under  full  sail,  if  applied 
in  the  direction  of  its  motion,  would  actually  increase 
its  speed,  although  the  effect  might  be  too  small  to  be 
visible.  Still  it  is  something,  and  may  be  truly  ex- 
pressed by  a  fraction.  Thus,  suppose  a  globe,  weigh- 
ing a  million  of  pounds,  were  suspended  from  the  ceil- 
ing by  a  string,  and  we  should  apply  to  it  the  snap  of  a 
finger, — it  is  granted  that  the  motion  would  be  quite 
insensible.  Let  us  then  divide  the  body  into  a  million 
equal  parts,  each  weighing  one  pound ;  then  the  same 
impulse,  applied  to  each  one  separately,  would  produce 
a  sensible  effect,  moving  it,  say  one  inch.  It  will  be 
found,  on  trial,  that  the  same  impulse  given  to  a  mass 
of  two  pounds  will  move  it  half  an  inch  ;  and  hence  it  is 
inferred,  that,  if  applied  to  a  mass  weighing  a  million 
of  pounds,  it  would  move  it  the  millionth  part  of  an  inch. 

It  is  one  of  the  curious  results  of  the  second  law  of 
motion,  that  an  unlimited  number  of  motions  may  exist 
together  in  the  same  body.  Thus,  at  the  same  moment^ 
we  may  be  walking  around  a  post  in  the  cabin  of  a 
steam-boat,  accompanying  the  boat  in  its  passage  around 
an  island,  revolving  with  the  earth  on  its  axis,  flying 
through  space  in  our  annual  circuit  around  the  sun,  and 
possibly  wheeling,  along  with  the  sun  and  his  whole 
retinue  of  planets,  around  some  centre  in  common  with 
the  starry  worlds. 

The  THIRD  LAW  of  motion  is  this :  action  and  reac- 
tion are  equal,  and  in  contrary  directions. 

Whenever  I  give  a  blow,  the  body  struck  exerts  an 
equal  force  on  the  striking  body.  If  I  strike  the  water 
with  an  oar,  the  water  communicates  an  equal  impulse 
to  the  oar,  which,  being  communicated  to  the  boat, 
drives  it  forward  in  the  opposite  direction.  If  a  magnet 
attracts  a  piece  of  iron,  the  iron  attracts  the  magnet 
just  as  much,  in  the  opposite  direction ;  and,  in  short, 
every  portion  of  matter  in  the  universe  attracts  and  is 
attracted  by  every  other,  equally,  in  an  opposite  direc- 
tion. This  brings  us  to  the  doctrine  of  universal  gravi- 
12  L.  A. 


134  LETTERS  ON  ASTRONOMY. 

tation,  which  is  the  very  key  that  unlocks  all  the  secrets 
of  the  skies.  This  will  form  the  subject  of  my  next 
Letter. 


LETTER  XIII. 

TERRESTRIAL  GRAVITY. 

"  To  Him  no  high,  no  low,  no  great,  no  small, 
He  fills,  He  bounds,  connects,  and  equals  all." — Pope. 

WE  discover  in  Nature  a  tendency  of  every  portion 
of  matter  towards  every  other.  This  tendency  is  called 
gravitation.  In  obedience  to  this  power,  a  stone  falls 
to  the  ground,  and  a  planet  revolves  around  the  sun. 
We  may  contemplate  this  subject  as  it  relates  either 
to  phenomena  that  take  place  near  the  surface  of  the 
earth,  or  in  the  celestial  regions.  The  former,  gravity, 
is  exemplified  by  falling  bodies ;  the  latter,  universal 
gravitation,  by  the  motions  of  the  heavenly  bodies. 
The  laws  of  terrestrial  gravity  were  first  investigated  by 
Galileo ;  those  of  universal  gravitation,  by  Sir  Isaac 
Newton.  Terrestrial  gravity  is  only  an  individual  ex- 
ample of  universal  gravitation  ;  being  the  tendency  of 
bodies  towards  the  centre  of  the  earth.  We  are  so 
much  accustomed,  from  our  earliest  years,  to  see  bodies 
fall  to  the  earth,  that  we  imagine  bodies  must  of  neces- 
sity fall  "  downwards ;"  but  when  we  reflect  that  the 
earth  is  round,  and  that  bodies  fall  towards  the  centre 
on  all  sides  of  it,  and  that  of  course  bodies  on  opposite 
sides  of  the  earth  fall  in  precisely  opposite  directions, 
and  towards  each  other,  we  perceive  that  there  must 
be  some  force  acting  to  produce  this  effect ;  nor  is  it 
enough  to  say,  as  the  ancients  did,  that  bodies  "  natur- 
ally" fall  to  the  earth.  Every  motion  implies  some 
force  which  produces  it ;  and  the  fact  that  bodies  fall 
towards  the  earth,  on  all  sides  of  it,  leads  us  to  infer 
that  that  force,  whatever  it  is,  resides  in  the  earth  itself. 


TERRESTRIAL  GRAVITY,  135 

We  therefore  call  it  attraction.  We  do  not,  however, 
say  what  attraction  is,  but  what  it  does.  We  must  bear 
in  mind,  also,  that,  according  to  the  third  law  of  mo- 
tion, this  attraction  is  mutual ;  that  when  a  stone  falls 
towards  the  earth,  it  exerts  the  same  force  on  the  earth 
that  the  earth  exerts  on  the  stone ;  but  the  motion  of 
the  earth  towards  the  stone  is  as  much  less  than  that  of 
the  stone  towards  the  earth,  as  its  quantity  of  matter  is 
greater ;  and  therefore  its  motion  is  quite  insensible. 

But  although  we  are  compelled  to  acknowledge  the 
existence  of  such  a  force  as  gravity,  causing  a  tendency 
in  all  bodies  towards  each  other,  yet  we  know  nothing 
of  its  nature,  nor  can  we  conceive  by  what  medium 
bodies  at  such  a  distance  as  the  moon  and  the  earth  ex- 
ercise this  influence  on  each  other.  Still,  we  may  trace 
the  modes  in  which  this  force  acts ;  that  is,  its  laws ; 
for  the  laws  of  Nature  are  nothing  else  than  the  modes 
in  which  the  powers  of  Nature  act. 

We  owe  chiefly  to  the  great  Galileo  the  first  investi- 
gation of  the  laws  of  terrestrial  gravity,  as  exemplified 
in  falling  bodies  ;  and  I  will  avail  myself  of  this  oppor- 
tunity to  make  you  better  acquainted  with  one  of  the 
most  interesting  of  men  and  greatest  of  philosophers. 

Galileo  was  born  at  Pisa,  in  Italy,  in  the  year  1564. 
He  was  the  son  of  a  Florentine  nobleman,  and  was  des- 
tined by  his  -father  for  the  medical  profession,  and  to 
this  his  earlier  studies  were  devoted.  But  a  fondness 
and  a  genius  for  mechanical  inventions  had  developed 
itself,  at  a  very  early  age,  in  the  construction  of  his 
toys,  and  a  love  of  drawing ;  and  as  he  grew  older,  a 
passion  for  mathematics,  and  for  experimental  research, 
predominated  over  his  zeal  for  the  study  of  medicine, 
and  he  fortunately  abandoned  that  for  the  more  conge- 
nial pursuits  of  natural  philosophy  and  astronomy.  In 
the  twenty-fifth  year  of  his  age,  he  was  appointed,  by 
the  Grand  Duke  of  Tuscany,  professor  of  mathematics 
in  the  University  of  Pisa.  At  that  period,  there  pre- 
vailed in  all  the  schools  a  most  extraordinary  reverence 
for  the  writings  of  Aristotle,  the  preceptor  of  Alexander 


136  LETTERS  ON  ASTRONOMY. 

the  Great, — a  philosopher  who  flourished  in  Greece, 
about  three  hundred  years  before  the  Christian  era. 
Aristotle,  by  his  great  genius  and  learning,  gained  a 
wonderful  ascendency  over  the  minds  of  men,  and  be- 
came the  oracle  of  the  whole  reading  world  for  twenty 
centuries.  It  was  held,  on  the  one  hand,  that  all  truths 
worth  knowing  were  contained  in  the  writings  of  Aris- 
totle ;  and,  on  the  other,  that  an  assertion  which  con- 
tradicted any  thing  in  Aristotle  could  not  be  true.  But 
Galileo  had  a  greatness  of  mind  which  soared  above 
the  prejudices  of  the  age  in  which  he  lived,  and  dared 
to  interrogate  Nature  by  the  two  great  and  only  suc- 
cessful methods  of  discovering  her  secrets, — experiment 
and  observation.  Galileo  was  indeed  the  first  philos- 
opher that  ever  fully  employed  experiments  as  the 
means  of  learning  the  laws  of  Nature,  by  imitating  on 
a  small  what  she  performs  on  a  great  scale,  and  thus 
detecting  her  modes  of  operation.  Archimedes,  the 
great  Sicilian  philosopher,  had  in  ancient  times  intro- 
duced mathematical  or  geometrical  reasoning  into  nat- 
ural philosophy  ;  but  it  was  reserved  for  Galileo  to  unite 
the  advantages  of  both  mathematical  and  experimental 
reasonings  in  the  study  of  Nature, — both  sure  and  the 
only  sure  guides  to  truth,  in  this  department  of  knowl- 
edge, at  least.  Experiment  and  observation  furnish  ma- 
terials upon  which  geometry  builds  her  reasonings,  and 
from  which  she  derives  many  truths  that  either  lie  for 
ever  hidden  from  the  eye  of  observation,  or  which  it 
would  require  ages  to  unfold. 

This  method,  of  interrogating  Nature  by  experiment 
and  observation,  was  matured  into  a  system  by  Lord 
Bacon,  a  celebrated  English  philosopher,  early  in  the 
seventeenth  century, — indeed,  during  the  life  of  Gali- 
leo.  Previous  to  that  time,  the  inquirers  into  Nature 
did  not  open  their  eyes  to  see  how  the  facts  really  are ; 
but,  by  metaphysical  processes,  in  imitation  of  Aristotle, 
determined  how  they  ought  to  be,  and  hastily  concluded 
that  they  were  so.  Thus,  they  did  not  study  into  the 
laws  of  motion,  by  observing  how  motion  actually  takes 


TERRESTRIAL  GRAVITY.  137 

place,  under  various  circumstances,  but  first,  in  their 
closets,  constructed  a  definition  of  motion,  and  thence 
inferred  all  its  properties.  The  system  of  reasoning  re- 
specting the  phenomena  of  Nature,  introduced  by  Lord 
Bacon,  was  this :  in  the  first  place,  to  examine  all  the 
facts  of  the  case,  and  then  from  these  to  determine  the 
laws  of  Nature.  To  derive  general  conclusions  from  the 
comparison  of  a  great  number  of  individual  instances 
constitutes  the  peculiarity  of  the  Baconian  philosophy. 
It  is  called  the  inductive  system,  because  its  conclusions 
were  built  on  the  induction,  or  comparison,  of  a  great 
many  single  facts.  Previous  to  the  time  of  Lord  Bacon, 
hardly  any  insight  had  been  gained  into  the  causes  of 
natural  phenomena,  and  hardly  one  of  the  laws  of  Na- 
ture had  been  clearly  established,  because  all  the  in- 
quirers into  Nature  were  upon  a  wrong  road,  groping 
their  way  through  the  labyrinth  of  error.  Bacon  point- 
ed out  to  them  the  true  path,  and  held  before  them  the 
torch-light  of  experiment  and  observation,  under  whose 
guidance  all  successful  students  of  Nature  have  since 
walked,  and  by  whose  illumination  they  have  gained  so 
wonderful  an  insight  into  the-  mysteries  of  the  natural 
world. 

It  is  a  remarkable  fact,  that  two  such  characters  as 
Bacon  and  Galileo  should  appear  on  the  stage  at  the 
same  time,  who,  without  any  communication  with  each 
other,  or  perhaps  without  any  personal  knowledge  of 
each  other's  existence,  should  have  each  developed  the 
true  method  of  investigating  the  laws  of  Nature.  Gali- 
leo practised  what  Bacon  only  taught ;  and  some,  there- 
fore, with  much  reason,  consider  Galileo  as  a  greater  phi- 
losopher than  Bacon.  "  Bacon,"  says  Hume,  "  pointed 
out,  at  a  great  distance,  the  road  to  philosophy  ;  Galileo 
both  pointed  it  out  to  others,  and  made,  himself,  consid- 
erable advances  in  it.  The  Englishman  was  ignorant 
of  geometry ;  the  Florentine  revived  that  science,  ex- 
celled in  it,  and  was  the  first  who  applied  it,  together 
with  experiment,  to  natural  philosophy.  The  former 
rejected,  with  the  most  positive  disdain,  the  system  of 


138  LETTERS  ON  ASTRONOMY. 

Copernicus  :  the  latter  fortified  it  with  new  proofs,  de- 
rived both  from  reason  and  the  senses." 

When  we  reflect  that  geometry  is  a  science  built 
upon  self-evident  truths,  and  that  all  its  conclusions  are 
the  result  of  pure  demonstration,  and  can  admit  of  no 
controversy  ;  when  we  further  reflect,  that  experimental 
evidence  rests  on  the  testimony  of  the  senses,  and  we 
infer  a  thing  to  be  true  because  we  actually  see  it  to  be 
so ;  it  shows  us  the  extreme  bigotry,  the  darkness  visi- 
ble, that  beclouded  the  human  intellect,  when  it  not 
only  refused  to  admit  conclusions  first  established  by 
pure  geometrical  reasoning,  and  afterwards  confirmed 
by  experiments  exhibited  in  the  light  of  day,  but  insti- 
tuted the  most  cruel  persecutions  against  the  great  phi- 
losopher who  first  proclaimed  these  truths.  Galileo 
was  hated  and  persecuted  by  two  distinct  bodies  of 
men,  both  possessing  great  influence  in  their  respective 
spheres, — the  one  consisting  of  the  learned  doctors  of 
philosophy,  who  did  nothing  more,  from  age  to  age, 
than  reiterate  the  doctrines  of  Aristotle,  and  were  conse- 
quently alarmed  at  the  promulgation  of  principles  sub- 
versive of  those  doctrines ;  the  other  consisting  of  the 
Romish  priesthood,  comprising  the  terrible  Inquisition, 
who  denounced  the  truths  taught  by  Galileo,  as  incon- 
sistent with  certain  declarations  of  the  Holy  Scriptures. 
We  shall  see,  as  we  advance,  what  a  fearful  warfare  he 
had  to  wage  against  these  combined  powers  of  darkness. 

Aristotle  had  asserted,  that,  if  two  different  weights 
of  the  same  material  were  let  fall  from  the  same  height, 
the  heavier  one  would  reach  the  ground  sooner  than 
the  other,  in  proportion  as  it  was  more  weighty.  For 
example :  if  a  ten-pound  leaden  weight  and  a  one- 
pound  were  let  fall  from  a  given  height  at  the  same 
instant,  the  former  would  reach  the  ground  ten  times 
as  soon  as  the  latter.  No  one  thought  of  making  the 
trial,  but  it  was  deemed  sufficient  that  Aristotle  had 
said  so ;  and  accordingly  this  assertion  had  long  been 
received  as  an  axiom  in  the  science  of  motion.  Galileo 
ventured  to  appeal  from  the  authority  of  Aristotle  to  that 


TERRESTRIAL  GRAVITY.  139 

of  his  own  senses,  and  maintained,  that  both  weights 
would  fall  in  the  same  time.  The  learned  doctors  ridi- 
culed the  idea.  Galileo  tried  the  experiment  in  their 
presence,  by  letting  fall,  at  the  same  instant,  large  and 
small  weights  from  the  top  of  the  celebrated  leaning 
tower  of  Pisa.  Yet,  with  the  sound  of  the  two  weights 
clicking  upon  the  pavement  at  the  same  moment,  they 
still  maintained  that  the  ten-pound  weight  would  reach 
the  ground  in  one  tenth  part  of  the  time  of  the  other, 
because  they  could  quote  the  chapter  and  verse  of  Aris- 
totle where  the  fact  was  asserted.  Wearied  and  dis- 
gusted with  the  malice  and  folly  of  these  Aristotelian 
philosophers,  Galileo,  at  the  age  of  twenty-eight,  re- 
signed his  situation  in  the  university  of  Pisa,  and  remov- 
ed to  Padua,  in  the  university  of  which  place  he  was 
elected  professor  of  mathematics.  Up  to  this  period, 
Galileo  had  devoted  himself  chiefly  to  the  studies  of  the 
laws  of  motion,  and  the  other  branches  of  mechanical 
philosophy.  Soon  afterwards,  he  began  to  publish  his 
writings,  in  rapid  succession,  and  became  at  once  among 
the  most  conspicuous  of  his  age, — a  rank  which  he 
afterwards  well  sustained  and  greatly  exalted,  by  the 
invention  of  the  telescope,  and  by  his  numerous  astro- 
nomical discoveries.  I  will  reserve  an  account  of  these 
great  achievements  until  we  come  to  that  part  of  as- 
tronomy to  which  they  were  more  immediately  related, 
and  proceed,  now,  to  explain  to  you  the  leading  prin- 
ciples of  terrestrial  gravity,  as  exemplified  in  falling 
bodies. 

First,  all  bodies  near  the  earth's  surface  fall  in 
straight  lines  towards  the  centre  of  the  earth.  We 
are  not  to  infer  from  this  fact,  that  there  resides  at  the 
centre  any  peculiar  force,  as  a  great  loadstone,  for  ex- 
ample, which  attracts  bodies  towards  itself ;  but  bodies 
fall  towards  the  centre  of  the  sphere,  because  the  com- 
bined attractions  of  all  the  particles  of  matter  in  the 
earth,  each  exerting  its  proper  force  upon  the  body, 
would  carry  it  towards  the  centre.  This  may  be  easily  il- 
lustrated by  a  diagram.  Let  B,  Fig.  29,  page  140,  be  the 


140 


LETTERS  ON  ASTRONOMY. 


centre  of  the  earth,  and  A  a  body 
without  it.  Every  portion  of  mat- 
ter in  the  earth  exerts  some  force 
on  A,  to  draw  it  down  to  the  earth. 
But  since  there  is  just  as  much 
matter  on  one  side  of  the  line  A  B. 
as  on  the  other  side,  each  half  ex- 
erts an  equal  force  to  draw  the 
body  towards  itself;  therefore  it 
falls  in  the  direction  of  the  diago- 
nal between  the  two  forces.  Thus, 
if  we  compare  the  effects  of  any 
two  particles  of  matter  at  equal  distances  from  the  line 
A  B,  but  on  opposite  sides  of  it,  as  a,  b,  while  the  force 
of  the  particle  at  a  would  tend  to  draw  A  in  the  direc- 
tion of  A  a,  that  of  b  would  draw  it  in  the  direction  of 
A  b,  and  it  would  fall  in  the  line  A  B,  half  way  be- 
tween the  two.  The  same  would  hold  true  of  any- 
other  two  corresponding  particles  of  matter  on  differ- 
ent sides  of  the  earth,  in  respect  to  a  body  situated  in 
any  place  without  it. 

Secondly,  all  bodies  fall  towards  the  earth,  from 
the  same  height,  with  equal  velocities.  A  musket-ball, 
and  the  finest  particle  of  down,  if  let  fall  from  a  certain 
height  towards  the  earth,  tend  to  descend  towards  it  at 
the  same  rate,  and  would  proceed  with  equal  speed, 
were  it  not  for  the  resistance  of  the  air,  which  retards 
the  down  more  than  it  does  the  ball,  and  finally  stops 
it.  If,  however,  the  air  be  removed  out  of  the  way,  as 
it  may  be  by  means  of  the  air-pump,  the  two  bodies 
keep  side  by  side  in  falling  from  the  greatest  height  at 
which  we  can  try  the  experiment. 

Thirdly,  bodies,  in  falling  towards  the  earth,  have 
their  rate  of  motion  continually  accelerated.  Sup- 
pose we  let  fall  a  musket-ball  from  the  top  of  a  high 
tower,  and  watch  its  progress,  disregarding  the  resist- 
ance of  the  air :  the  first  second,  it  will  pass  over  six- 
teen feet  and  one  inch,  but  its  speed  will  be  constant- 
ly increased,  being  all  the  while  urged  onward  by  the 


TERRESTRIAL  GRAVITY.  141 

same  force,  and  retaining  all  that  it  has  already  acquir- 
ed ;  so  that  the  longer  it  is  in  falling,  the  swifter  its 
motion  becomes.  Consequently,  when  bodies  fall  from 
a  great  height,  they  acquire  an  immense  velocity  be- 
fore they  reach  the  earth.  Thus,  a  man  falling  from  a 
balloon,  or  from  the  mast-head  of  a  ship,  is  broken  in 
pieces ;  and  those  meteoric  stones,  which  sometimes 
fall  from  the  sky,  bury  themselves  deep  in  the  earth. 
On  measuring  the  spaces  through  which  a  body  falls, 
it  is  found,  that  it  will  fall  four  times  as  far  in  two  sec- 
onds as  in  one,  and  one  hundred  times  as  far  in  ten 
seconds  as  in  one ;  and  universally,  the  space  describ- 
ed by  a  falling  body  is  proportioned  to  the  time  multi- 
plied into  itself ;  that  is,  to  the  square  of  the  time. 

Fourthly,  gravity  is  proportioned  to  the  quantity  of 
matter.  A  body  which  has  twice  as  much  matter  as 
another  exerts  a  force  of  attraction  twice  as  great,  and 
also  receives  twice  as  much  from  the  same  body  as  it 
would  do,  if  it  were  only  just  as  heavy  as  that  body. 
Thus  the  earth,  containing,  as  it  does,  forty  times  as 
much  matter  as  the  moon,  exerts  upon  the  moon  forty 
times  as  much  force  as  it  would  do,  were  its  mass  the 
same  with  that  of  the  moon ;  but  it  is  also  capable  of 
receiving  forty  times  as  much  gravity  from  the  moon  as 
it  would  do,  were  its  mass  the  same  as  the  moon's ;  so 
that  the  power  of  attracting  and  that  of  being  attracted 
are  reciprocal ;  and  it  is  therefore  correct  to  say,  that 
the  moon  attracts  the  earth  just  as  much  as  the  earth 
attracts  the  moon  ;  arid  the  same  may  be  said  of  any 
two  bodies,  however  different  in  quantity  of  matter. 

Fifthly,  gravity,  when  acting  at  a  distance  from 
the  earth,  is  not  as  intense  as  it  is  near  the  earth.  At 
such  a  distance  as  we  are  accustomed  to  ascend  above 
the  general  level  of  the  earth,  no  great  difference  is  ob- 
served. On  the  tops  of  high  mountains,  we  find  bodies 
falling  towards  the  earth,  with  nearly  the  same  speed 
as  they  do  from  the  smallest  elevations.  It  is  found, 
nevertheless,  that  there  is  a  real  difference  ;  so  that,  in 
fact,  the  weight  of  a  body  (which  is  nothing  more 


142  LETTERS   ON  ASTRONOMY. 

than  the  measure  of  its  force  of  gravity)  is  not  quite 
so  great  on  the  tops  of  high  mountains  as  at  the  general 
level  of  the  sea.  Thus,  a  thousand  pounds'  weight,  on 
the  top  of  a  mountain  half  a  mile  high,  would  weigh 
a  quarter  of  a  pound  less  than  at  the  level  of  the  sea ; 
and  if  elevated  four  thousand  miles  above  the  earth, — 
that  is,,  twice  as  far  from  the  centre  of  the  earth  as  the 
surface  is  from  the  centre, — it  would  weigh  only  one 
fourth  as  much  as  before  ;  if  three  times  as  far,  it  would 
weigh  only  one  ninth  as  much.  So  that  the  force  of 
gravity  decreases,  as  we  recede  from  the  earth,  in  the 
same  proportion  as  the  square  of  the  distance  increases. 
This  fact  is  generalized  by  saying,  that  the  force  of 
gravity,  at  different  distances  from  the  earth,  is  in- 
versely as  the  square  of  the  distance. 

Were  a  body  to  fall  from  a  great  distance, — suppose  a 
thousand  times  that  of  the  radius  of  the  earth, — the  force 
of  gravity  being  one  million  times  less  than  that  at  the 
surface  of  the  earth,  the  motion  of  the  body  would  be 
exceedingly  slow,  carrying  it  over  only  the  sixth  part 
of  an  inch  in  a  day.  It  would  be  a  long  time,  there- 
fore, in  making  any  sensible  approaches  towards  the 
earth  ;  but  at  length,  as  it  drew  near  to  the  earth  it 
would  acquire  a  very  great  velocity,  and  would  finally 
rush  towards  it  with  prodigious  violence.  Falling  so 
far,  and  being  continually  accelerated  on  the  way,  we 
might  suppose  that  it  would  at  length  attain  a  veloci- 
ty infinitely  great ;  but  it  can  be  demonstrated,  that, 
if  a  body  were  to  fall  from  an  infinite  distance,  attract- 
ed to  the  earth  only  by  gravity,  it  could  never  acquire 
a  velocity  greater  than  about  seven  miles  per  second. 
This,  however,  is  a  speed  inconceivably  great,  being 
about  eighteen  times  the  greatest  velocity  that  can  be 
given  to  a  cannon-ball,  and  more  than  twenty-five  thous- 
and miles  per  hour. 

But  the  phenomena  of  falling  bodies  must  have 
long  been  observed,  and  their  laws  had  been  fully  in- 
vestigated by  Galileo  and  others,  before  the  cause  of 
their  falling  was  understood,  or  any  such  principle  as 


SIR  ISAAC  NEWTON.  143 

gravity,  inherent  in  the  earth  and  in  all  bodies,  was  ap- 
plied to  them.  The  developement  of  this  great  prin- 
ciple was  the  work  of  Sir  Isaac  Newton ;  and  I  will 
give  you,  in  my  next  Letter,  some  particulars  respecting 
the  life  and  discoveries  of  this  wonderful  man. 


LETTER  XIV. 

SIR  ISAAC  NEWTON. UNIVERSAL  GRAVITATION. FIGURE  OP 

THE  EARTH'S  ORBIT. — PRECESSION  OF  THE  EQUINOXES. 

"  The  heavens  are  all  his  own  ;  from  the  wild  rule 
Of  whirling  vortices,  and  circling  spheres, 
To  their  first  great  simplicity  restored. 
The  schools  astonished  stood  ;  but  found  it  vain 
To  combat  long  with  demonstration  clear, 
And,  unawakened.  dream  beneath  the  blaze 
Of  truth.     At  once  their  pleasing  visions  fled, 
With  the  light  shadows  of  the  morning  mixed, 
When  Newton  rose,  our  philosophic  sun." — Thomson's  Elegy. 

SIR  ISAAC  NEWTON  was  born  in  Lincolnshire,  Eng- 
land, in  1642,  just  one  year  after  the  death  of  Galileo. 
His  father  died  before  he  was  born,  and  he  was  a  help- 
less infant,  of  a  diminutive  size,  and  so  feeble  a  frame, 
that  his  attendants  hardly  expected  his  life  for  a  single 
hour.  The  family  dwelling  was  of  humble  architec- 
ture, situated  in  a  retired  but  beautiful  valley,  and  was 
surrounded  by  a  small  farm,  which  afforded  but  a  scanty 
living  to  the  widowed  mother  and  her  precious  charge. 
The  cut  on  page  144,  Fig  30,  represents  the  modest 
mansion,  and  the  emblems  of  rustic  life  that  first  met 
the  eyes  of  this  pride  of  the  British  nation,  and  orna- 
ment of  human  nature.  It  will  probably  be  found,  that 
genius  has  oftener  emanated  from  the  cottage  than  from 
the  palace. 

The  boyhood  of  Newton  was  distinguished  chiefly  for 
his  ingenious  mechanical  contrivances.  Among  other 
pieces  of  mechanism,  he  constructed  a  windmill  so  cu- 
rious and  complete  in  its  workmanship,  as  to  excite  uni- 
versal admiration.  After  carrying  it  a  while  by  the  force 


144 


LETTERS   ON  ASTRONOMY. 

Fig.  30. 


of  the  wind,  he  resolved  to  substitute  animal  power; 
and  for  this  purpose  he  inclosed  in  it  a  mouse,  which 
he  called  the  miller,  and  which  kept  the  mill  a-going  by 
acting  on  a  tread-wheel.  The  power  of  the  mouse 
was  brought  into  action  by  unavailing  attempts  to 
reach  a  portion  of  corn  placed  above  the  wheel.  A 
water-clock,  a  four-wheeled  carriage  propelled  by  the 
rider  himself,  and  kites  of  superior  workmanship,  were 
among  the  productions  of  the  mechanical  genius  of 
this  gifted  boy.  At  a  little  later  period,  he  began  to 
turn  his  attention  to  the  motions  of  the  heavenly  bod- 
ies, and  constructed  several  sun-dials  on  the  walls  of  the 
house  where  he  lived.  All  this  was  before  he  had 
reached  his  fifteenth  year.  At  this  age,  he  was  sent 
by  his  mother,  in  company  with  an  old  family  servant, 
to  a  neighboring  market-town,  to  dispose  of  products 
of  their  farm,  and  to  buy  articles  of  merchandise  for 
their  family  use  ;  but  the  young  philosopher  left  all 
these  negotiations  to  his  worthy  partner,  occupying 
himself,  mean-while,  with  a  collection  of  old  books, 
which  he  had  found  in  a  garret.  At  other  times,  he 
stopped  on  the  road,  and  took  shelter  with  his  book 
under  a  hedge,  until  the  servant  returned.  They  en- 


SIR  ISAAC  NEWTON.  145 

deavored  to  educate  him  as  a  farmer ;  but  the  perusal 
of  a  book,  the  construction  of  a  water-mill,  or  some 
other  mechanical  or  scientific  amusement,  absorbed  all 
his  thoughts,  when  the  sheep  were  going  astray,  and 
the  cattle  were  devouring  or  treading  down  the  corn. 
One  of  his  uncles  having  found  him  one  day  under  a 
hedge,  with  a  book  in  his  hand,  and  entirely  absorbed 
in  meditation,  took  it  from  him,  and  found  that  it  was 
a  mathematical  problem  which  so  engrossed  his  atten- 
tion. His  friends,  therefore,  wisely  resolved  to  favor 
the  bent  of  his  genius,  and  removed  him  from  the  farm 
to  the  school,  to  prepare  for  the  university.  In  the 
eighteenth  year  of  his  age,  Newton  was  admitted  into 
Trinity  College,  Cambridge.  He  made  rapid  and  ex- 
traordinary advances  in  the  mathematics,  and  soon  af- 
forded unequivocal  presages  of  that  greatness  which  af- 
terwards placed  him  at  the  head  of  the  human  intellect. 
In  1669,  at  the  age  of  twenty-seven,  he  became  pro- 
fessor of  mathematics  at  Cambridge,  a  post  which  he 
occupied  for  many  years  afterwards.  During  the  four 
or  five  years  previous  to  this  he  had,  in  fact,  made  most 
of  those  great  discoveries  which  have  immortalized  his 
name.  We  are  at  present  chiefly  interested  in  one  of 
these,  namely,  that  of  universal  gravitation;  and  let 
us  see  by  what  steps  he  was  conducted  to  this  greatest 
of  scientific  discoveries. 

In  the  year  1666,  when  Newton  was  about  twenty- 
four  years  of  age,  the  plague  was  prevailing  at  Cam- 
bridge, and  he  retired  into  the  country.  One  day,  while 
he  sat  in  a  garden,  musing  on  the  phenomena  of  Nature 
around  him,  an  apple  chanced  to  fall  to  the  ground.  Re- 
flecting on  the  mysterious  power  that  makes  all  bodies 
near  the  earth  fall  towards  its  centre,  and  considering 
that  this  power  remains  unimpaired  at  considerable 
heights  above  the  earth,  as  on  the  tops  of  trees  and  moun- 
tains, he  asked  himself, — "  May  not  the  same  force  ex- 
tend its  influence  to  a  great  distance  from  the  earth,  even 
as  far  as  the  moon  ?  Indeed,  may  not  this  be  the  very 
reason,  why  the  moon  is  drawn  away  continually  from 
13  L.  A. 


146  LETTERS  ON  ASTRONOMY. 

the  straight  line  in  which  every  body  tends  to  move,  and 
is  thus  made  to  circulate  around  the  earth  ?"  You  will 
recollect  that  it  was  mentioned,  in  my  Letter  which  con- 
tained an  account  of  the  first  law  of  motion,  that  if  a 
body  is  put  in  motion  by  any  force,  it  will  always  move 
forward  in  a  straight  line,  unless  some  other  force  com- 
pels it  to  turn  aside  from  such  a  direction  ;  and  that,  when 
we  see  a  body  moving  in  a  curve,  as  a  circular  orbit,  we 
are  authorized  to  conclude  that  there  is  some  force  ex- 
isting within  the  circle,  which  continually  draws  the 
body  away  from  the  direction  in  which  it  tends  to  move. 
Accordingly,  it  was  a  very  natural  suggestion,  to  one 
so  well  acquainted  with  the  laws  of  motion  as  Newton, 
that  the  moon  should  constantly  bend  towards  the  earth, 
from  a  tendency  to  fall  towards  it,  as  any  other  heavy 
body  would  do,  if  carried  to  such  a  distance  from  the 
earth.  Newton  had  already  proved,  that  if  such  a  pow- 
er as  gravity  extends  from  the  earth  to  distant  bodies,  it 
must  decrease,  as  the  square  of  the  distance  from  the 
centre  of  the  earth  increases ;  that  is,  at  double  the  dis- 
tance, it  would  be  four  times  less ;  at  ten  times  the  dis- 
tance, one  hundred  times  less  ;  and  so  on.  Now,  it 
was  known  that  the  moon  is  about  sixty  times  as  far 
from  the  centre  of  the  earth  as  the  surface  of  the  earth 
is  from  the  centre,  and  consequently,  the  force  of  attrac- 
tion at  the  moon  must  be  the  square  of  sixty,  or  thirty-six 
hundred  times  less  than  it  is  at  the  earth  ;  so  that  a  body 
at  the  distance  of  the  moon  would  fall  towards  the 
earth  very  slowly,  only  one  thirty-six  hundredth  part  as 
far  in  a  given  time,  as  at  the  earth.  Does  the  moon  ac- 
tually fall  towards  the  earth  at  this  rate ;  or,  what  is  the 
same  thing,  does  she  depart  at  this  rate  continually  from 
the  straight  line  in  which  she  tends  to  move,  and  in 
which  she  would  move,  if  no  external  force  diverted  her 
from  it  ?  On  making  the  calculation,  such  was  found 
to  be  the  fact.  Hence  gravity,  and  no  other  force  than 
gravity,  acts  upon  the  moon,  and  compels  her  to  revolve 
around  the  earth.  By  reasonings  equally  conclusive,  it 
was  afterwards  proved,  that  a  similar  force  compels  all 


UNIVERSAL  GRAVITATION.  147 

the  planets  to  circulate  around  the  sun ;  and  now,  we 
may  ascend  from  the  contemplation  of  this  force,  as  we 
have  seen  it  exemplified  in  falling  bodies,  to  that  of  a 
universal  power  whose  influence  extends  to  all  the  ma- 
terial creation.  It  is  in  this  sense  that  we  recognise  the 
principle  of  universal  gravitation,  the  law  of  which  may 
be  thus  enunciated ;  all  bodies  in  the  universe,  wheth- 
er great  or  small,  attract  each  other,  with  forces  pro- 
portioned to  their  respective  quantities  of  matter,  and 
inversely  as  the  squares  of  their  distances  from  each 
other. 

This  law  asserts,  first,  that  attraction  reigns  through- 
out the  material  world,  affecting  alike  the  smallest  par- 
ticle of  matter  and  the  greatest  body ;  secondly,  that 
it  acts  upon  every  mass  of  matter,  precisely  in  propor- 
tion to  its  quantity  ;  and,  thirdly,  that  its  intensity  is  di- 
minished as  the  square  of  the  distance  is  increased. 

Observation  has  fully  confirmed  the  prevalence  of  this 
law  throughout  the  solar  system  ;  and  recent  discoveries 
among  the  fixed  stars,  to  be  more  fully  detailed  hereaf- 
ter, indicate  that  the  same  law  prevails  there.  The  law 
of  universal  gravitation  is  therefore  held  to  be  the  grand 
principle  which  governs  all  the  celestial  motions.  Not 
only  is  it  consistent  with  all  the  observed  motions  of  the 
heavenly  bodies,  even  the  most  irregular  of  those  mo- 
tions, but,  when  followed  out  into  all  its  consequences, 
it  would  be  competent  to  assert  that  such  irregularities 
must  take  place,  even  if  they  had  never  been  observed. 

Newton  first  published  the  doctrine  of  universal  grav- 
itation in  the  '  Principia,'  in  1687.  The  name  implies 
that  the  work  contains  the  fundamental  principles  of 
natural  philosophy  and  astronomy.  Being  founded  up- 
on the  immutable  basis  of  mathematics,  its  conclusions 
must  of  course  be  true  and  unalterable,  and  thenceforth 
we  may  regard  the  great  laws  of  the  universe  as  traced 
to  their  remotest  principle.  The  greatest  astronomers 
and  mathematicians  have  since  occupied  themselves  in 
following  out  the  plan  which  Newton  began,  by  applying 
the  principles  of  universal  gravitation  to  all  the  subordi- 


148  LETTERS  ON  ASTRONOMY. 

nate  as  well  as  to  the  grand  movements  of  the  spheres. 
This  great  labor  has  been  especially  achieved  by  La 
Place,  a  French  mathematician  of  the  highest  eminence, 
in  his  profound  work,  the  '  Mecanique  Celeste.'  Of  this 
work,  our  distinguished  countryman,  Dr.  Bowditch,  has 
given  a  magnificent  translation,  and  accompanied  it  with 
a  commentary,  which  both  illustrates  the  original,  and 
adds  a  great  amount  of  matter  hardly  less  profound 
than  that. 

We  have  thus  far  taken  the  earth's  orbit  around  the 
sun  as  a  great  circle,  such  being  its  projection  on  the 
sphere  constituting  the  celestial  ecliptic.  The  real  path 
of  the  earth  around  the  sun  is  learned,  as  I  before  ex- 
plained to  you,  by  the  apparent  path  of  the  sun  around 
the  earth  once  a  year.  Now,  when  a  body  revolves 
about  the  earth  at  a  great  distance  from  us,  as  is  the 
case  with  the  sun  and  moon,  we  cannot  certainly  infer 
that  it  moves  in  a  circle  because  it  appears  to  describe 
a  circle  on  the  face  of  the  sky,  for  such  might  be  the 
appearance  of  its  orbit,  were  it  ever  so  irregular  a  curve. 
Thus,  if  E,  Fig.  31,  represents  the  earth,  and  A  CB, 

Fig.  31. 


the  irregular  path  of  a  body  revolving  about  it,  since  we 
should  refer  the  body  continually  to  some  place  on  the 
celestial  sphere,  X  Y  Z,  determined  by  lines  drawn 
from  the  eye  to  the  concave  sphere  through  the  body, — 


FIGURE   OF  THE   EARTH  S  ORBIT. 


149 


the  body,  while  moving  from  A  to  B  through  C,  would 
appear  to  move  from  X  to  Z,  through  Y.  Hence,  we 
must  determine  from  other  circumstances  than  the  actual 
appearance,  what  is  the  true  figure  of  the  orbit. 

Were  the  earth's  path  a  circle,  having  the  sun  in  the 
centre,  the  sun  would  always  appear  to  be  at  the  same 
distance  from  us  ;  that  is,  the  radius  of  the  orbit,  or  ra- 
dius vector.,  (the  name  given  to  a  line  drawn  from 
the  centre  of  the  sun  to  the  orbit  of  any  planet,)  would 
always  be  of  the  same  length.  But  the  earth's  distance 
from  the  sun  is  constantly  varying,  which  shows  that 
its  orbit  is  not  a  circle.  We  learn  the  true  figure  of 
the  orbit,  by  ascertaining  the  relative  distances  of  the 
earth  from  the  sun,  at  various  periods  of  the  year. 
These  distances  all  being  laid  down  in  a  diagram,  ac- 
cording to  their  respective  lengths,  the  extremities,  on 
being  connected,  give  us  our  first  idea  of  the  shape  of 
the  orbit,  which  appears  of  an  oval  form,  and  at  least 
resembles  an  ellipse ;  and,  on  further  trial,  we  find 
that  it  has  the  properties  of  an  ellipse.  Thus,  let  E, 
Fig.  32,  be  the  place  of  the  earth,  and  o,  6,  c,  &c.,  suc- 

Fig.  32. 


cessive  positions  of  the  sun ;  the  relative  lengths  of  the 
lines  E  a,  E  6,  &c.,  being  known,  on  connecting  the 
13* 


150  LETTERS  ON   ASTRONOMY. 

points  a,  &,  c,  &c.,  the  resulting  figure  indicates  the 
true  figure  of  the  earth's  orbit. 

These  relative  distances  are  found  in  two  different 
ways  ;  first,  by  changes  in  the  sun's  apparent  diameter. 
and,  secondly,  by  variations  in  his  angular  velocity. 
The  same  object  appears  to  us  smaller  in  proportion  as 
it  is  more  distant ;  and  if  we  see  a  heavenly  body  vary- 
ing in  size,  at  different  times,  we  infer  that  it  is  at  dif- 
ferent distances  from  us ;  that  when  largest,  it  is  near- 
est to  us,  and  when  smallest,  furthest  off.  Now,  when 
the  sun's  diameter  is  accurately  measured  by  instru- 
ments, it  is  found  to  vary  from  day  to  day ;  being, 
when  greatest,  more  than  thirty-two  minutes  and  a 
half,  and  when  smallest,  only  thirty-one  minutes  and 
a  half, — differing,  in  all,  about  seventy-five  seconds. 
When  the  diameter  is  greatest,  which  happens  in  Jan- 
uary, we  know  that  the  sun  is  nearest  to  us ;  and  when 
the  diameter  is  least,  which  occurs  in  July,  we  infer  that 
the  sun  is  at  the  greatest  distance  from  us.  The  point 
where  the  earth,  or  any  planet,  in  its  revolution,  is  near- 
est the  sun,  is  called  its  perihelion ;  the  point  where  it 
is  furthest  from  the  sun,  its  aphelion.  Suppose,  then, 
that,  about  the  first  of  January,  when  the  diameter  of 
the  sun  is  greatest,  we  draw  a  line,  E  a,  Fig,  32,  to 
represent  it,  and  afterwards,  every  ten  days,  draw  other 
lines,  E  b,  E  c,  &c. ;  increasing  in  the  same  ratio  as 
the  apparent  diameters  of  the  sun  decrease.  These 
lines  must  be  drawn  at  such  a  distance  from  each  oth- 
er, that  the  triangles,  E  a  b,  E  b  c,  &c.,  shall  be  all  equal 
to  each  other,  for  a  reason  that  will  be  explained  here- 
after. On  connecting  the  extremities  of  these  lines,  we 
shall  obtain  the  figure  of  the  earth's  orbit. 

Similar  conclusions  may  be  drawn  from  observations 
on  the  sun's  angular  velocity.  A  body  appears  to 
move  most  rapidly  when  nearest  to  us.  Indeed,  the 
apparent  velocity  increases  rapidly,  as  it  approaches  us, 
and  as  rapidly  diminishes,  when  it  recedes  from  us.  If 
it  comes  twice  as  near  as  before,  it  appears  to  move  not 
merely  twice  as  swiftly,  but  four  times  as  swiftly ;  if  it 


151 

comes  ten  times  nearer,  its  apparent  velocity  is  one  hun- 
dred times  as  great  as  before.  We  say,  therefore,  that 
the  velocity  varies  inversely  as  the  square  of  the  dis- 
tance ;  for,  as  the  distance  is  diminished  ten  times,  the 
velocity  is  increased  the  square  of  ten  ;  that  is,  one  hun- 
dred times.  Now,  by  noting  the  time  it  takes  the  sun, 
from  day  to  day,  to  cross  the  central  wire  of  the  transit- 
instrument,  we  learn  the  comparative  velocities  with 
which  it  moves  at  different  times ;  and  from  these  we 
derive  the  comparative  distances  of  the  sun  at  the  cor- 
responding times  ;  and  laying  down  these  relative  dis- 
tances in  a  diagram,  as  before,  we  get  our  first  notions 
of  the  actual  figure  of  the  earth's  orbit,  or  the  path 
which  it  describes  in  its  annual  revolution  around  the 
sun. 

Having  now  learned  the  fact,  that  the  earth  moves 
around  the  sun,  not  in  a  circular  but  in  an  elliptical 
orbit,  you  will  desire  to  know  by  what  forces  it  is  im- 
pelled, to  make  it  describe  this  figure,  with  such  unifor- 
mity and  constancy,  from  age  to  age.  It  is  commonly 
said,  that  gravity  causes  the  earth  and  the  planets  to 
circulate  around  the  sun ;  and  it  is  true  that  it  is  gravi- 
ty which  turns  them  aside  from  the  straight  line  in 
which,  by  the  first  law  of  motion,  they  tend  to  move, 
and  thus  causes  them  to  revolve  around  the  sun.  But 
what  force  is  that  which  gave  to  them  this  original  im- 
pulse, and  impressed  upon  them  such  a  tendency  to 
move  forward  in  a  straight  line  ?  The  name  projectile 
force  is  given  to  it,  because  it  is  the  same  as  though  the 
earth  were  originally  projected  into  space,  when  first 
created ;  and  therefore  its  motion  is  the  result  of  two 
forces,  the  projectile  force,  which  would  cause  it  to 
move  forward  in  a  straight  line  which  is  a  tangent  to 
its  orbit,  and  gravitation,  which  bends  it  towards  the 
sun.  But  before  you  can  clearly  understand  the  nature 
of  this  motion,  and  the  action  of  the  two  forces  that 
produce  it,  I  must  explain  to  you  a  few  elementary 
principles  upon  which  this  and  all  the  other  planetary 
motions  depend. 


152  LETTERS  ON  ASTRONOMY. 

You  have  already  learned,  that  when  a  body  is  act- 
ted  on  by  two  forces,  in  different  directions,  it  moves 
in  the  direction  of  neither,  but  in  some  direction  be- 
tween them.  If  I  throw  a  stone  horizontally,  the  at- 
traction of  the  earth  will  continually  draw  it  downward, 
out  of  the  line  of  direction  in  which  it  was  thrown,  and 
make  it  descend  to  the  earth  in  a  curve.  The  particu- 
lar form  of  the  curve  will  depend  on  the  velocity  with 
which  it  is  thrown.  It  will  always  begin  to  move  in 
the  line  of  direction  in  which  it  is  projected;  but  it 
will  soon  be  turned  from  that  line  towards  the  earth.  It 
will,  however,  continue  nearer  to  the  line  of  projection 
in  proportion  as  the  velocity  of  projection  is  greater. 
Thus,  let  A  C,  Fig.  33,  be  perpendicular  to  the  horizon, 

Fig.  33. 


and  A  B  parallel  to  it,  and  let  a  stone  be  thrown  from 
A,  in  the  direction  of  A  B.  It  will,  in  every  case,  com- 
mence its  motion  in  the  line  A  B,  which  will  therefore 
be  a  tangent  to  the  curve  it  describes  ;  but,  if  it  is  thrown 
with  a  small  velocity,  it  will  soon  depart  from  the  tan- 
gent, describing  the  line  A  D ;  with  a  greater  velocity, 
it  will  describe  a  curve  nearer  the  tangent,  as  A  E  ;  and 
with  a  still  greater  velocity,  it  will  describe  the  curve 
AF. 

As  an  example  of  a  body  revolving  in  an  orbit  i*.«. 
the  influence  of  two  forces,  suppose  a  body  placv 
any  point,  P,  Fig.  34,  above  the  surface  of  the  earth, 
and  let  P  A  be  the  direction  of  the  earth's  centre  ;  that 
is,  a  line  perpendicular  to  the  horizon.     If  the  body 
were  allowed  to  move,  without  receiving  any  impulse, 


153 


it  would  descend  to  the  earth  in  the  direction  P  A  with 
an  accelerated  motion.  But  suppose  that,  at  the  mo- 
ment of  its  departure  from  P,  it  receives  a  blow  in  the 
direction  P  B,  which  would  carry  it  to  B  in  the  time  the 
body  would  fall  from  P  to  A  ;  then,  under  the  influence 
of  both  forces,  it  would  descend  along  the  curve  P  D. 
If  a  stronger  blow  were  given  to  it  in  the  direction  P  B, 
it  would  describe  a  larger  curve,  P  E ;  or,  finally,  if 
the  impulse  were  sufficiently  strong,  it  would  circulate 
quite  around  the  earth,  and  return  again  to  P,  describ- 
ing the  circle  P  F  G.  With  a  velocity  of  projection 
still  greater,  it  would  describe  an  ellipse,  P I  K  ;  and  if 
the  velocity  be  increased  to  a  certain  degree,  the  figure 
becomes  a  parabola,  L  P  M, — a  curve  which  never  re- 
turns into  itself. 

In  Fig.  35,  page  154,  suppose  the  planet  to  have  passed 
the  point  C,  at  the  aphelion,  with  so  small  a  velocity,  that 
the  attraction  of  the  sun  bends  its  path  very  much,  and 
onuses  it  immediately  to  begin  to  approach  towards  the 
~$ftf,r  The  sun's  attraction  will  increase  its  velocity,  as 
K  tg^ves  through  D,  E,  and  F,  for  the  sun's  attractive 
force"  on  the  planet,  when  at  D,  is  acting  in  the  direction 
D  S ;  and,  on  account  of  the  small  angle  made  between 
D  E  and  D  S,  the  force  acting  in  the  line  D  S  helps  the 
planet  forward  in  the  path  D  E,  and  thus  increases  its 


154 


LETTERS  ON  ASTRONOMY. 


I) 


FiS-  35-  velocity.      In  like  manner, 

the  velocity  of  the  planet 
will  be  continually  increas- 
ing as  it  passes  through  D, 
E,  and  F  ;  and  though  the 
attractive  force,  on  account 
of  the  planet's  nearness,  is 
so  much  increased,  and 
tends,  therefore,  to  make 
the  orbit  more  curved,  yet 
the  velocity  is  also  so  much 
increased,  that  the  orbit  is 
not  more  curved  than  be- 
fore ;  for  the  same  increase 
of  velocity,  occasioned  by  the  planet's  approach  to  the 
sun,  produces  a  greater  increase  of  centrifugal  force, 
which  carries  it  off  again.  We  may  see,  also,  the  rea- 
son why,  when  the  planet  has  reached  the  most  distant 
parts  of  its  orbit,  it  does  not  entirely  fly  off,  and  never 
return  to  the  sun ;  for,  when  the  planet  passes  along 
H,  K,  A,  the  sun's  attraction  retards  the  planet,  just  as 
gravity  retards  a  ball  rolled  up  hill ;  and  when  it  has 
reached  C,  its  velocity  is  very  small,  and  the  attraction 
to  the  centre  of  force  causes  a  great  deflection  from  the 
tangent,  sufficient  to  give  its  orbit  a  great  curvature,  and 
the  planet  wheels  about,  returns  to  the  sun,  and  goes 
over  the  same  orbit  again.  As  the  planet  recedes  from 
the  sun,  its  centrifugal  force  diminishes  faster  than  the  , 
force  of  gravity,  so  that  the  latter  finally  preponderates,  a 
I  shall  conclude  what  I  have  to  say  at  present,  respect-  <j 
ing  the  motion  of  the  earth  around  the  sun,  by  adding 
a  few  words  respecting  the  precession  of  the  equinoxes. 
The  precession  of  the  equinoxes  is  a  slow  but  con- 
tinual shifting  of  the  equinoctial  points,  from  east  to 
west.  Suppose  that  we  mark  the  exact  place  in  the 
heavens  where,  during  the  present  year,  the  sun  crosses 
the  equator,  and  that  this  point  is  close  to  a  certain  star  ; 
next  year,  the  sun  will  cross  the  equator  a  little  way  west- 
ward of  that  star,  and  so  every  year,  a  little  further  west- 


PRECESSION  OF  THE  EQUINOXES.         155 

ward,  until,  in  a  long  course  of  ages,  the  place  of  the 
equinox  will  occupy  successively  every  part  of  the  eclip- 
tic, until  we  come  round  to  the  same  star  again.  As, 
therefore,  the  sun  revolving  from  west  to  east,  in  his  ap- 
parent orbit,  comes  round  to  the  point  where  it  left  the 
equinox,  it  meets  the  equinox  before  it  reaches  that 
point.  The  appearance  is  as  though  the  equinox  goes 
forward  to  meet  the  sun,  and  hence  the  phenomenon 
is  called  the  precession  of  the  equinoxes  ;  and  the  fact 
is  expressed  by  saying,  that  the  equinoxes  retrograde  on 
the  ecliptic,  until  the  line  of  the  equinoxes  (a  straight 
line  drawn  from  one  equinox  to  the  other)  makes  a  com- 
plete revolution,  from  east  to  west.  This  is  of  course 
a  retrograde  motion,  since  it  is  contrary  to  the  order  of 
the  signs.  The  equator  is  conceived  as  sliding  west- 
ward on  the  ecliptic,  always  preserving  the  same  in- 
clination to  it,  as  a  ring,  placed  at  a  small  angle  with 
another  of  nearly  the  same  size  which  remains  fixed, 
may  be  slid  quite  around  it,  giving  a  corresponding  mo- 
tion to  the  two  points  of  intersection.  It  must  be  ob- 
served, however,  that  this  mode  of  conceiving  of  the 
precession  of  the  equinoxes  is  purely  imaginary,  and  is 
employed  merely  for  the  convenience  of  representation. 

The  amount  of  precession  annually  is  fifty  seconds 
and  one  tenth ;  whence,  since  there  are  thirty-six  hun- 
dred seconds  in  a  degree,  and  three  hundred  and  six- 
ty degrees  in  the  whole  circumference  of  the  ecliptic, 
and  consequently  one  million  two  hundred  and  ninety- 
-ix  thousand  seconds,  this  sum,  divided  by  fifty  seconds 
.nd  one  tenth,  gives  twenty-five  thousand  eight  hundred 
and  sixty-eight  years  for  the  period  of  a  complete  revo- 
lution of  the  equinoxes. 

Suppose  we  now  fix  to  the  centre  of  each  of  the  two 
rings,  before  mentioned,  a  wire  representing  its  axis,  one 
corresponding  to  the  axis  of  the  ecliptic,  the  other  to 
that  of  the  equator,  the  extremity  of  each  being  the  pole 
of  its  circle.  As  the  ring  denoting  the  equator  turns 
round  on  the  ecliptic,  which,  with  its  axis,  remains  fixed, 
it  is  easy  to  conceive  that  the  axis  of  the  equator  revolves 


156  LETTERS  ON  ASTRONOMY. 

around  that  of  the  ecliptic,  and  the  pole  of  the  equator 
around  the  pole  of  the  ecliptic,  and  constantly  at  a  dis- 
tance equal  to  the  inclination  of  the  two  circles.  To 
transfer  our  conceptions  to  the  celestial  sphere,  we  may 
easily  see  that  the  axis  of  the  diurnal  sphere  (that  of  the 
earth  produced)  would  not  have  its  pole  constantly  in 
the  same  place  among  the  stars,  but  that  this  pole  would 
perform  a  slow  revolution  around  the  pole  of  the  eclip- 
tic, from  east  to  west,  completing  the  circuit  in  about 
twenty-six  thousand  years.  Hence  the  star  which  we 
now  call  the  pole-star  has  not  always  enjoyed  that  dis- 
tinction, nor  will  it  always  enjoy  it,  hereafter.  When 
the  earliest  catalogues  of  the  stars  were  made,  this  star 
was  twelve  degrees  from  the  pole.  It  is  now  one  degree 
twenty-four  minutes,  and  will  approach  still  nearer  ;  or, 
to  speak  more  accurately,  the  pole  will  come  still  near- 
er to  this  star,  after  which  it  will  leave  it,  and  success- 
ively pass  by  others.  In  about  thirteen  thousand  years, 
the  bright  star  Lyra  (which  lies  near  the  circle  in  which 
the  pole  of  the  equator  revolves  about  the  pole  of  the 
ecliptic,  on  the  side  opposite  to  the  present  pole-star) 
will  be  within  five  degrees  of  the  pole,  and  will  consti- 
tute the  pole-star.  As  Lyra  now  passes  near  our  zenith, 
you  might  suppose  that  the  change  of  position  of  the 
pole  among  the  stars  would  be  attended  with  a  change 
of  altitude  of  the  north  pole  above  the  horizon.  This 
mistaken  idea  is  one  of  the  many  misapprehensions 
which  result  from  the  habit  of  considering  the  horizon 
as  a  fixed  circle  in  space.  However  the  pole  might 
shift  its  position  in  space,  we  should  still  be  at  the  same 
distance  from  it,  and  our  horizon  would  always  reach  the 
same  distance  beyond  it. 

The  time  occupied  by  the  sun,  in  passing  from  the 
equinoctial  point  round  to  the  same  point  again,  is  call- 
ed the  tropical  year.  As  the  sun  does  not  perform  a 
complete  revolution  in  this  interval,  but  falls  short  of  it 
fifty  seconds  and  one  tenth,  the  tropical  year  is  shorter 
than  the  sidereal  by  twenty  minutes  and  twenty  sec- 
onds, in  mean  solar  time,  this  being  the  time  of  describ- 


THE   MOON.  157 

ing  an  arc  of  fifty  seconds  and  one  tenth,  in  the  annual 
revolution. 

The  changes  produced  by  the  precession  of  the  equi- 
noxes, in  the  apparent  places  of  the  circumpolar  stars, 
have  led  to  some  interesting  results  in  chronology.  In 
consequence  of  the  retrograde  motion  of  the  equinoc- 
tial points,  the  signs  of  the  ecliptic  do  not  correspond, 
at  present,  to  the  constellations  which  bear  the  same 
names,  but  lie  about  one  sign,  or  thirty  degrees,  west- 
ward of  them.  Thus,  that  division  of  the  ecliptic  which 
is  called  the  sign  Taurus  lies  in  the  constellation  Aries, 
and  the  sign  Gemini,  in  the  constellation  Taurus.  Un- 
doubtedly, however,  when  the  ecliptic  was  thus  first  di- 
vided, and  the  divisions  named,  the  several  constella- 
tions lay  in  the  respective  divisions  which  bear  their 
names. 


LETTER  XV. 

THE  MOON. 

14  Soon  as  the  evening  shades  prevail 
The  Moon  takes  up  the  wondrous  tale, 
And  nightly  to  the  listening  earth 
Repeats  the  story  of  her  birth." — Addison. 

HAVING  now  learned  so  much  of  astronomy  as  re- 
lates to  the  earth  and  the  sun,  and  the  mutual  relations 
which  exist  between  them,  you  are  prepared  to  enter 
with  advantage  upon  the  survey  of  the  other  bodies  that 
compose  the  solar  system.  This  being  done,  we  shall 
then  have  still  before  us  the  boundless  range  of  the 
fixed  stars. 

The  moon,  which  next  claims  our  notice,  has  been 
studied  by  astronomers  with  greater  attention  than  any 
other  of  the  heavenly  bodies,  since  her  comparative 
nearness  to  the  earth  brings  her  peculiarly  within  the 
range  of  our  telescopes,  and  her  periodical  changes  and 
very  irregular  motions,  afford  curious  subjects,  both  for 
observation  and  speculation.  The  mild  light  of  the 

14  L.  A. 


158  LETTERS   ON  ASTRONOMY. 

moon  also  invites  our  gaze,  while  her  varying  aspects 
serve  barbarous  tribes,  especially,  for  a  kind  of  dial- 
plate  inscribed  on  the  face  of  the  sky,  for  weeks,  and 
months,  and  times,  and  seasons. 

The  moon  is  distant  from  the  earth  about  two  hun- 
dred and  forty  thousand  miles ;  or,  more  exactly,  two 
hundred  and  thirty-eight  thousand  five  hundred  and 
forty-five  miles.  Her  angular  or  apparent  diameter  is 
about  half  a  degree,  and  her  real  diameter,  two  thous- 
and one  hundred  and  sixty  miles.  She  is  a  compan- 
ion, or  satellite,  to  the  earth,  revolving  around  it  every 
month,  and  accompanying  us  in  our  annual  revolution 
around  the  sun.  Although  her  nearness  to  us  makes 
her  appear  as  a  large  and  conspicuous  object  in  the 
heavens,  yet,  in  comparison  with  most  of  the  other  ce- 
lestial bodies,  she  is  in  fact  very  small,  being  only  one 
forty-ninth  part  as  large  as  the  earth,  and  only  about  one 
seventy  millionth  part  as  large  as  the  sun. 

The  moon  shines  by  light  borrowed  from  the  sun, 
being  itself  an  opaque  body,  like  the  earth.  When  the 
disk,  or  any  portion  of  it,  is  illuminated,  we  can  plainly 
discern,  even  with  the  naked  eye,  varieties  of  light  and 
shade,  indicating  inequalities  of  surface  which  we  im- 
agine to  be  land  and  water.  I  believe  it  is  the  common 
impression,  that  the  darker  portions  are  land  and  the 
lighter  portions  water;  but  if  either  part  is  water,  it 
must  be  the  darker  regions.  A  smooth  polished  sur- 
face, like  water,  would  reflect  the  sun's  light  like  a  mir- 
ror. It  would,  like  a  convex  mirror,  form  a  diminished 
image  of  the  sun,  but  would  not  itself  appear  luminous 
like  an  uneven  surface,  which  multiplies  the  light  by 
numerous  reflections  within  itself.  Thus,  from  this 
cause,  high  broken  mountainous  districts  appear  more 
luminous  than  extensive  plains. 

By  the  aid  of  the  telescope,  we  may  see  undoubted 
indications  of  mountains  and  valleys.  Indeed,  with  a 
good  glass,  we  can  discover  the  most  decisive  evidence 
that  the  surface  of  the  moon  is  exceedingly  varied, — 
one  part  ascending  in  lofty  peaks,  another  clustering  in 


Figures  36,  37. 


TELESCOPIC  VIEWS    OF    THE    MOON. 


THE  MOON.  159 

huge  mountain  groups,  or  long  ranges,  and  another 
bearing  all  the  marks  of  deep  caverns  or  valleys.  You 
will  not,  indeed,  at  the  first  sight  of  the  moon  through 
a  telescope,  recognise  all  these  different  objects.  If 
you  look  at  the  moon  when  half  her  disk  is  enlight- 
ened, (which  is  the  best  time  for  seeing  her  varieties 
of  surface,)  you  will,  at  the  first  glance,  observe  a  mot- 
ley appearance,  particularly  along  the  line  called  the 
terminator,  which  separates  the  enlightened  from  the 
unenlightened  part  of  the  disk.  (Fig.  37.)  On  one 
side  of  the  terminator,  within  the  dark  part  of  the 
disk,  you  will  see  illuminated  points,  and  short,  crooked 
lines,  like  rude  characters  marked  with  chalk  on  a  black 
ground.  On  the  other  side  of  the  terminator  you  will 
see  a  succession  of  little  circular  groups,  appearing  like 
numerous  bubbles  of  oil  on  the  surface  of  water.  The 
further  you  carry  your  eye  from  the  terminator,  on  the 
same  side  of  it,  the  more  indistinctly  formed  these  bub- 
bles appear,  until  towards  the  edge  of  the  moon  they 
assume  quite  a  different  aspect. 

Some  persons,  when  they  look  into  a  telescope  for 
the  first  time,  having  heard  that  mountains  and  valleys 
are  to  be  seen,  and  discovering  nothing  but  these  un- 
meaning figures,  break  off  in  disappointment,  and  have 
their  faith  in  these  things  rather  diminished  than  in- 
creased. I  would  advise  you,  therefore,  before  you 
take  even  your  first  view  of  the  moon  through  a  teles- 
cope, to  form  as  clear  an  idea  as  you  can,  how  moun- 
tains, and  valleys,  and  caverns,  situated  at  such  a  dis- 
tance from  the  eye,  ought  to  look,  and  by  what  marks 
they  may  be  recognised.  Seize,  if  possible,  the  most 
favorable  period,  (about  the  time  of  the  first  quarter,) 
and  previously  learn  from  drawings  and  explanations, 
how  to  interpret  every  thing  you  see. 

What,  then,  ought  to  be  the  respective  appearances 
of  mountains,  valleys,  and  deep  craters,  or  caverns,  in 
the  moon  ?  The  sun  shines  on  the  moon  in  the  same 
way  as  it  shines  on  the  earth  ;  and  let  us  reflect,  then, 
upon  the  manner  in  which  it  strikes  similar  objects  here. 


160  LETTERS  ON  ASTRONOMY. 

One  half  the  globe  is  constantly  enlightened  ;  and,  by 
the  revolution  of  the  earth  on  its  axis,  the  terminator, 
or  the  line  which  separates  the  enlightened  from  the 
unenlightened  part  of  the  earth,  travels  along  from 
east  to  west,  over  different  places,  as  we  see  the  moon's 
terminator  travel  over  her  disk  from  new  to  full  moon ; 
although,  in  the  case  of  the  earth,  the  motion  is  more 
rapid,  and  depends  on  a  different  cause.  In  the  morn- 
ing, the  sun's  light  first  strikes  upon  the  tops  of  the 
mountains,  and,  if  they  are  very  high,  they  may  be 
brightly  illuminated  while  it  is  yet  night  in  the  valleys 
below.  By  degrees,  as  the  sun  rises,  the  circle  of  illu- 
mination travels  down  the  mountain,  until  at  length  it 
reaches  the  bottom  of  the  valleys ;  and  these  in  turn 
enjoy  the  full  light  of  day.  Again,  a  mountain  casts  a 
shadow  opposite  to  the  sun,  which  is  very  long  when 
the  sun  first  rises,  and  shortens  continually  as  the  sun 
ascends,  its  length  at  a  given  time,  however,  being  pro- 
portioned to  the  height  of  the  mountain  ;  so  that,  if  the 
shadow  be  still  very  long  when  the  sun  is  far  above  the 
horizon,  we  infer  that  the  mountain  is  very  lofty.  We 
may,  moreover,  form  some  judgement  of  the  shape  of 
a  mountain,  by  observing  that  of  its  shadow. 

Now,  the  moon  is  so  distant  that  we  could  not  easily 
distinguish  places  simply  by  their  elevations,  since  they 
would  be  projected  into  the  same  imaginary  plane  which 
constitutes  the  apparent  disk  of  the  moon  ;  but  the  fore- 
going considerations  would  enable  us  to  infer  their  ex- 
istence. Thus,  when  you  view  the  moon  at  any  time 
within  her  first  quarter,  but  better  near  the  end  of  that 
period,  you  will  observe,  on  the  side  of  the  terminator 
within  the  dark  part  of  the  disk,  the  tops  of  moun- 
tains which  the  light  of  the  sun  is  just  striking,  as  the 
morning  sun  strikes  the  tops  of  mountains  on  the  earth. 
These  you  will  recognise  by  those  white  specks  and 
little  crooked  lines,  before  mentioned,  as  is  represent- 
ed in  Fig.  37.  These  bright  points  and  lines  you  will 
see  altering  their  figure,  every  hour,  as  they  come 
more  and  more  into  the  sun's  light;  and,  mean-while. 


THE  MOON.  161 

other  bright  points,  very  minute  at  first,  will  start  into 
view,  which  also  in  turn  grow  larger  as  the  termi- 
nator approaches  them,  until  they  fall  into  the  enlight- 
ened part  of  the  disk.  As  they  fall  further  and  further 
within  this  part,  you  will  have  additional  proofs  that 
they  are  mountains,  from  the  shadows  which  they  cast 
on  the  plain,  always  in  a  direction  opposite  to  the  sun. 
The  mountain  itself  may  entirely  disappear,  or  become 
confounded  with  the  other  enlightened  portions  of  the 
surface  ;  but  its  position  and  its  shape  may  still  be  rec- 
ognised by  the  dark  line  which  it  projects  on  the  plane. 
This  line  will  correspond  in  shape  to  that  of  the  moun- 
tain, presenting  at  one  time  a  long  serpentine  stripe  of 
black,  denoting  that  the  mountain  is  a  continued  range ; 
at  another  time  exhibiting  a  conical  figure  tapering  to  a 
point,  or  a  series  of  such  sharp  points ;  or  a  serrated,  un- 
even termination,  indicating,  in  each  case  respectively, 
a  conical  mountain,  or  a  group  of  peaks,  or  a  range  with 
lofty  cliffs.  All  these  appearances  will  indeed  be  seen 
in  miniature ;  but  a  little  familiarity  with  them  will  en- 
able you  to  give  them,  in  imagination,  their  proper  di- 
mensions, as  you  give  to  the  pictures  of  known  animals 
their  due  sizes,  although  drawn  on  a  scale  far  below 
that  of  real  life. 

In  the  next  place,  let  us  see  how  valleys  and  deep 
craters  in  the  moon  might  be  expected  to  appear.  We 
could  not  expect  to  see  depressions  any  more  than  ele- 
vations, since  both  would  alike  be  projected  on  the  same 
imaginary  disk.  But  we  may  recognise  such  depres- 
sions, from  the  manner  in  which  the  light  of  the  sun 
shines  into  them.  When  we  hold  a  china  tea-cup  at 
some  distance  from  a  candle,  in  the  night,  the  candle  be- 
ing elevated  but  little  above  the  level  of  the  top  of  the 
cup,  a  luminous  crescent  will  be  formed  on  the  side  of 
the  cup  opposite  to  the  candle,  while  the  side  next  to  the 
candle  will  be  covered  by  a  deep  shadow.  As  we  grad- 
ually elevate  the  candle,  the  crescent  enlarges  and  travels 
down  the  side  of  the  cup,  until  finally  the  whole  interior 
becomes  illuminated.  We  observe  similar  appearances 
14* 


162  LETTERS  ON  ASTRONOMY. 

in  the  moon,  which  we  recognise  as  deep  depressions. 
They  are  those  circular  spots  near  the  terminator  before 
spoken  of,  which  look  like  bubbles  of  oil  floating  on 
water.  They  are  nothing  else  than  circular  craters  or 
deep  valleys.  When  they  are  so  situated  that  the  light 
of  the  sun  is  just  beginning  to  shine  into  them,  you  may 
see,  as  in  the  tea-cup,  a  luminous  crescent  around  the 
side  furthest  from  the  sun,  while  a  deep  black  shadow 
is  cast  on  the  side  next  to  the  sun.  As  the  cavity  is 
turned  more  and  more  towards  the  light,  the  crescent 
enlarges,  until  at  length  the  whole  interior  is  illuminat- 
ed. If  the  tea-cup  be  placed  on  a  table,  and  a  candle 
be  held  at  some  distance  from  it,  nearly  on  a  level  with 
the  top,  but  a  little  above  it,  the  cup  itself  will  cast 
a  shadow  on  the  table,  like  any  other  elevated  object 
In  like  manner,  many  of  these  circular  spots  on  the 
moon  cast  deep  shadows  behind  them,  indicating  that, 
the  tops  of  the  craters  are  elevated  far  above  the  gen- 
eral level  of  the  moon.  The  regularity  of  some  of 
these  circular  spots  is  very  remarkable.  The  circle,  in 
some  instances,  appears  as  well  formed  as  could  be  de- 
scribed by  a  pair  of  compasses,  while  in  the  centre  there 
not  unfrequently  is  seen  a  conical  mountain  casting  its 
pointed  shadow  on  the  bottom  of  the  crater.  I  hope 
you  will  enjoy  repeated  opportunities  to  view  the  moon 
through  a  telescope.  Allow  me  to  recommend  to  you, 
not  to  rest  satisfied  with  a  hasty  or  even  with  a  single 
view,  but  to  verify  the  preceding  remarks  by  repeated 
and  careful  inspection  of  the  lunar  disk,  at  different  ages 
of  the  moon. 

The  various  places  on  the  moon's  disk  have  received 
appropriate  names.  The  dusky  regions  being  formerly 
supposed  to  be  seas,  were  named  accordingly  ;  and  other 
remarkable  places  have  each  two  names,  one  derived 
from  some  well-known  spot  on  the  earth,  and  the  other 
from  some  distinguished  personage.  Thus,  the  same 
bright  spot  on  the  surface  of  the  moon  is  called  Mount 
Sinai  or  Tycho,  and  another,  Mount  Etna  or  Coper- 
nicus. The  names  of  individuals,  however,  are  more 


THE  MOON.  163 

used  than  the  others.  The  diagram,  Fig.  36,  (see  page 
159,)  represents  rudely,  the  telescopic  appearance  of 
the  full  moon.  The  reality  is  far  more  beautiful.  A 
few  of  the  most  remarkable  points  have  the  following 
names  corresponding  to  the  numbers  and  letters  on  the 
map. 

1.  Tycho,  6.  Eratosthenes, 

2.  Kepler,  7.  Plato, 

3.  Copernicus,  8.  Archimedes, 

4.  Aristarchus,  9.  Eudoxus, 

5.  Helicon,  10.  Aristotle. 

A.  Mare  Humorum,  Sea  of  Humors, 

B.  Mare  Nubium,  Sea  of  Clouds, 

C.  Mare  Imbrium,  Sea  of  Rains, 

D.  Mare  Nectaris,  Sea  of  Nectar, 

E.  Mare  Tranquillitatis,  Sea  of  Tranquillity) 

F.  Mare  Serenitatis,  Sea  of  Serenity, 

G.  Mare  Fecunditatis,  Sea  of  Plenty, 
H.  Mare  Crisium,  Crisian  Sea. 

The  heights  of  the  lunar  mountains,  and  the  depths 
of  the  valleys,  can  be  estimated  with  a  considerable  de- 
gree of  accuracy.  Some  of  the  mountains  are  as  high 
as  five  miles,  and  the  valleys,  in  some  instances,  are  four 
miles  deep.  Hence  it  is  inferred,  that  the  surface  of 
the  moon  is  more  broken  and  irregular  than  that  of  the 
earth,  its  mountains  being  higher  and  its  valleys  deeper, 
in  proportion  to  its  magnitude,  than  those  of  the  earth. 

The  varieties  of  surface  in  the  moon,  as  seen  by  the 
aid  of  large  telescopes,  have  been  well  described  by 
Dr.  Dick,  in  his  (  Celestial  Scenery,'  and  I  cannot  give 
you  a  better  idea  of  them,  than  to  add  a  few  extracts 
from  his  work.  The  lunar  mountains  in  general  exhibit 
an  arrangement  and  an  aspect  very  different  from  the 
mountain  scenery  of  our  globe.  They  may  be  arrang- 
ed under  the  four  following  varieties  : 

First,  insulated  mountains,  which  rise  from  plains 
nearly  level,  shaped  like  a  sugar  loaf,  which  may  be 
supposed  to  present  an  appearance  somewhat  similar 


164  LETTERS  ON  ASTRONOMY. 

to  Mount  Etna,  or  the  Peak  of  TenerifTe.  The  shad- 
ows of  these  mountains,  in  certain  phases  of  the  moon, 
are  as  distinctly  perceived  as  the  shadow  of  an  upright 
staff,  when  placed  opposite  to  the  sun  ;  and  these  heights 
can  be  calculated  from  the  length  of  their  shadows. 
Some  of  these  mountains  being  elevated  in  the  midst  of 
extensive  plains,  would  present  to  a  spectator  on  their 
summits  magnificent  views  of  the  surrounding  regions. 

Secondly,  mountain  ranges,  extending  in  length  two 
or  three  hundred  miles.  These  ranges  bear  a  distant  re- 
semblance to  our  Alps,  Apennines,  and  Andes  ;  but  they 
are  much  less  in  extent.  Some  of  them  appear  very 
rugged  and  precipitous ;  and  the  highest  ranges  are  in 
some  places  more  than  four  miles  in  perpendicular  alti- 
tude. In  some  instances,  they  are  nearly  in  a  straight 
line  from  northeast  to  southwest,  as  in  the  range  called 
the  Apennines  ;  in  other  cases,  they  assume  the  form  of 
a  semicircle,  or  crescent. 

Thirdly,  circular  ranges,  which  appear  on  almost 
every  part  of  the  moon's  surface,  particularly  in  its  south- 
ern regions.  This  is  one  grand  peculiarity  of  the  lunar 
ranges,  to  which  we  have  nothing  similar  on  the  earth. 
A  plain,  and  sometimes  a  large  cavity,  is  surrounded 
with  a  circular  ridge  of  mountains,  which  encompasses 
it  like  a  mighty  rampart.  These  annular  ridges  and 
plains  are  of  all  dimensions,  from  a  mile  to  forty  or  fifty 
miles  in  diameter,  and  are  to  be  seen  in  great  numbers 
over  every  region  of  the  moon's  surface  ;  they  are  most 
conspicuous,  however,  near  the  upper  and  lower  limbs, 
about  the  time  of  the  half  moon. 

The  mountains  which  form  these  circular  ridges  are 
of  different  elevations,  from  one  fifth  of  a  mile  to  three 
miles  and  a  half,  and  their  shadows  cover  one  half  of  the 
plain  at  the  base.  These  plains  are  sometimes  on  a  lev- 
el with  the  general  surface  of  the  moon,  and  in  other 
cases  they  are  sunk  a  mile  or  more  below  the  level  of 
the  ground  which  surrounds  the  exterior  circle  of  the 
mountains. 

Fourthly,  central  mountains,  or  those  which  are  plac- 


THE  MOON.  165 

ed  in  the  middle  of  circular  plains.  In  many  of  the  plains 
and  cavities  surrounded  by  circular  ranges  of  mountains 
there  stands  a  single  insulated  mountain,  which  rises 
from  the  centre  of  the  plain,  and  whose  shadow  some- 
times extends,  in  the  form  of  a  pyramid,  half  across 
the  plain  to  the  opposite  ridges.  These  central  moun- 
tains are  generally  from  half  a  mile  to  a  mile  and  a  half 
in  perpendicular  altitude.  In  some  instances,  they  have 
two,  and  sometimes  three,  different  tops,  whose  shad- 
ows can  be  easily  distinguished  from  each  other.  Some- 
times they  are  situated  towards  one  side  of  the  plain,  or 
cavity  ;  but  in  the  great  majority  of  instances  their  po- 
sition is  nearly  or  exactly  central.  The  lengths  of  their 
bases  vary  from  five  to  about  fifteen  or  sixteen  miles. 
The  lunar  caverns  form  a  very  peculiar  and  promi- 
nent feature  of  the  moon's  surface,  and  are  to  be  seen 
throughout  almost  every  region,  but  are  most  numerous 
in  the  southwest  part  of  the  moon.  Nearly  a  hundred 
of  them,  great  and  small,  may  be  distinguished  in  that 
quarter.  They  are  all  nearly  of  a  circular  shape,  and 
appear  like  a  very  shallow  egg-cup.  The  smaller  cav- 
ities appear,  within,  almost  like  a  hollow  cone,  with  the 
sides  tapering  towards  the  centre  ;  but  the  larger  ones 
have,  for  the  most  part,  flat  bottoms,  from  the  centre 
of  which  there  frequently  rises  a  small,  steep,  conical 
hill,  which  gives  them  a  resemblance  to  the  circular 
ridges  and  central  mountains  before  described.  In 
some  instances,  their  margins  are  level  with  the  gene- 
ral surface  of  the  moon  ;  but,  in  most  cases,  they  are  en- 
circled with  a  high  annular  ridge  of  mountains,  marked 
with  lofty  peaks.  Some  of  the  larger  of  these  cavities 
contain  smaller  cavities  of  the  same  kind  and  form,  par- 
ticularly in  their  sides.  The  mountainous  ridges  which 
surround  these  cavities  reflect  the  greatest  quantity  of 
light ;  and  hence  that  region  of  the  moon  in  which  they 
abound  appears  brighter  than  any  other.  From  their 
lying  in  every  possible  direction,  they  appear,  at  and 
near  the  time  of  full  moon,  like  a  number  of  brilliant 
streaks,  or  radiations.  These  radiations  appear  to  con- 


166  LETTERS   ON  ASTRONOMY. 

verge  towards  a  large  brilliant  spot,  surrounded  by  a 
faint  shade,  near  the  lower  part  of  the  moon,  which  is 
named  Tycho, — a  spot  easily  distinguished  even  by  a 
small  telescope.  The  spots  named  Kepler  and  Coper- 
nicus are  each  composed  of  a  central  spot  with  lumin- 
ous radiations.* 

The  broken  surface  and  apparent  geological  struc- 
ture of  the  moon  has  suggested  the  opinion,  that  the 
moon  has  been  subject  to  powerful  volcanic  action. 
This  opinion  receives  support  from  certain  actual  ap- 
pearances of  volcanic  fires,  which  have  at  different 
times  been  observed.  In  a  total  eclipse  of  the  sun,  the 
moon  comes  directly  between  us  and  that  luminary,  and 
presents  her  dark  side  towards  us  under  circumstances 
very  favorable  for  observation.  At  such  times,  several 
astronomers,  at  different  periods,  have  noticed  bright 
spots,  which  they  took  to  be  volcanoes.  It  must  evi- 
dently require  a  large  fire  to  be  visible  at  all,  at  such  a 
distance  ;  and  even  a  burning  spark,  or  point  but  just 
visible  in  a  large  telescope,  might  be  in  fact  a  volcano 
raging  like  Etna  or  Vesuvius.  Still,  as  fires  might  be 
supposed  to  exist  in  the  moon  from  different  causes, 
we  should  require  some  marks  peculiar  to  volcanic  fires, 
to  assure  us  that  such  was  their  origin  in  a  given  case. 
Dr.  Herschel  examined  this  point  with  great  attention, 
and  with  better  means  of  observation  than  any  of  his 
predecessors  enjoyed,  and  fully  embraced  the  opinion 
that  what  he  saw  were  volcanoes.  In  April,  1787,  he 
records  his  observations  as  follows :  "I  perceive  three 
volcanoes  in  different  places  in  the  dark  part  of  the 
moon.  Two  of  them  are  already  nearly  extinct,  or  oth- 
erwise in  a  state  of  going  to  break  out ;  the  third  shows 
an  eruption  of  fire  or  luminous  matter."  On  the  next 
night,  he  says :  "  The  volcano  burns  with  greater  vio- 
lence than  last  night ;  its  diameter  cannot  be  less  than 
three  seconds  ;  and  hence  the  shining  or  burning  mat- 
ter must  be  above  three  miles  in  diameter.  The  ap- 
pearance resembles  a  small  piece  of  burning  charcoal, 

*  Dick's  '  Celestial  Scenery,'  Chapter  IV. 


THE  MOON.  167 

when  it  is  covered  with  a  very  thin  coat  of  white  ashes ; 
and  it  has  a  degree  of  brightness  about  as  strong  as  that 
with  which  such  a  coal  would  be  seen  to  glow  in  faint 
daylight."  That  these  were  really  volcanic  fires,  he 
considered  further  evident  from  the  fact,  that  where  a 
fire,  supposed  to  have  been  volcanic,  had  been  burning, 
there  was  seen,  after  its  extinction,  an  accumulation  of 
matter,  such  as  would  arise  from  the  production  of  a 
great  quantity  of  lava,  sufficient  to  form  a  mountain. 

It  is  probable  that  the  moon  has  an  atmosphere,  al- 
though it  is  difficult  to  obtain  perfectly  satisfactory  evi- 
dence of  its  existence  ;  for  granting  the  existence  of  an 
atmosphere  bearing  the  same  proportion  to  that  planet 
as  our  atmosphere  bears  to  the  earth,  its  dimensions 
and  its  density  would  be  so  small,  that  we  could  detect 
its  presence  only  by  the  most  refined  observations.  As 
our  twilight  is  owing  to  the  agency  of  our  atmosphere, 
so,  could  we  discern  any  appearance  of  twilight  in  the 
moon,  we  should  regard  that  fact  as  indicating  that  she 
is  surrounded  by  an  atmosphere.  Or,  when  the  moon 
covers  the  sun  in  a  solar  eclipse,  could  we  see  around 
her  circumference  a  faint  luminous  ring,  indicating  that 
the  sunlight  shone  through  an  aerial  medium,  we  might 
likewise  infer  the  existence  of  such  a  medium.  Such 
a  faint  ring  of  light  has  sometimes,  as  is  supposed, 
been  observed.  Schroeter,  a  German  astronomer,  dis- 
tinguished for  the  acuteness  of  his  vision  and  his  pow- 
ers of  observation  in  general,  was  very  confident  of 
having  obtained,  from  different  sources,  clear  evidence 
of  a  lunar  atmosphere.  He  concluded,  that  the  infe- 
rior or  more  dense  part  of  the  moon's  atmosphere  is 
not  more  than  fifteen  hundred  feet  high,  and  that  the 
entire  height,  at  least  to  the  limit  where  it  would  be  too 
rare  to  produce  any  of  the  phenomena  which  are  relied 
on  as  proofs  of  its  existence,  is  not  more  than  a  mile. 

It  has  been  a  question,  much  agitated  among  astron- 
omers, whether  there  is  water  in  the  moon.  Analogy 
strongly  inclines  us  to  reply  in  the  affirmative.  But 
the  analogy  between  the  earth  and  the  moon,  as  deriv- 


168  LETTERS  ON  ASTRONOMY. 

ed  from  all  the  particulars  in  which  we  can  compare 
the  two  bodies,  is  too  feeble  to  warrant  such  a  conclu- 
sion, and  we  must  have  recourse  to  other  evidence,  be- 
fore we  can  decide  the  point.  In  the  first  place,  then, 
there  is  no  positive  evidence  in  favor  of  the  existence 
of  water  in  the  moon.  Those  extensive  level  regions, 
before  spoken  of,  and  denominated  seas  in  the  geogra- 
phy of  this  planet,  have  no  other  signs  of  being  water, 
except  that  they  are  level  and  dark.  But  both  these 
particulars  would  characterize  an  earthly  plain,  like  the 
deserts  of  Arabia  and  Africa.  In  the  second  place, 
were  those  dark  regions  composed  of  water,  the  termi- 
nator would  be  entirely  smooth  where  it  passed  over 
these  oceans  or  seas.  It  is  indeed  indented  by  few  in- 
equalities, compared  with  those  which  it  exhibits  where 
it  passes  over  the  mountainous  regions  ;  but  still,  the 
inequalities  are  too  considerable  to  permit  the  conclu- 
sion, that  these  level  spots  are  such  perfect  levels  as 
water  would  form.  They  do  not  appear  to  be  more 
perfect  levels  than  many  plain  countries  on  the  globe. 
The  deep  caverns,  moreover,  seen  in  those  dusky  spots 
which  were  supposed  to  be  seas,  are  unfavorable  to  the 
supposition  that  those  regions  are  covered  by  water.  In 
the  third  place,  the  face  of  the  moon,  when  illuminated 
by  the  sun  and  not  obscured  by  the  state  of  our  own 
atmosphere,  is  always  serene,  and  therefore  free  from 
clouds.  Clouds  are  objects  of  great  extent ;  they  fre- 
quently intercept  light,  like  solid  bodies ;  and  did  they 
exist  about  the  moon,  we  should  certainly  see  them, 
and  should  lose  sight  of  certain  parts  of  the  lunar  disk 
which  they  covered.  But  neither  position  is  true  ;  we 
neither  see  any  clouds  about  the  moon,  with  our  best 
telescopes,  nor  do  we,  by  the  intervention  of  clouds, 
ever  lose  sight  of  any  portion  of  the  moon  when  our 
own  atmosphere  is  clear.  But  the  want  of  clouds  in  the 
lunar  atmosphere  almost  necessarily  implies  the  absence 
of  water  in  the  moon.  This  planet  is  at  the  same  dis- 
tance from  the  sun  as  our  own,  and  has,  in  this  respect, 
on  equal  opportunity  to  feel  the  influence  of  his  rays. 


THE  MOON.  169 

Its  days  are  also  twenty-seven  times  as  long  as  ours, 
a  circumstance  which  would  augment  the  solar  heat. 
When  the  pressure  of  the  atmosphere  is  diminished  on 
the  surface  of  water,  its  tendency  to  pass  into  the  state 
of  vapor  is  increased.  Were  the  whole  pressure  of  the 
atmosphere  removed  from  the  surface  of  a  lake,  in  a 
Summer's  day,  when  the  temperature  was  no  higher 
than  seventy-two  degrees,  the  water  would  begin  to 
boil.  Now  it  is  well  ascertained,  that  if  there  be  any 
atmosphere  about  the  moon,  it  is  much  lighter  than 
ours,  and  presses  on  the  surface  of  that  body  with  a 
proportionally  small  force.  This  circumstance,  there- 
fore, would  conspire  with  the  other  causes  mentioned, 
to  convert  all  the  water  of  the  moon  into  vapor,  if  we 
could  suppose  it  to  have  existed  at  any  given  time. 

But  those,  who  are  anxious  to  furnish  the  moon  and 
other  planets  with  all  the  accommodations  which  they 
find  in  our  own,  have  a  subterfuge  in  readiness,  to 
which  they  invariably  resort  in  all  cases  like  the  fore- 
going. "  There  may  be,"  say  they,  "  some  means,  un- 
known to  us,  provided  for  retaining  water  on  the  sur- 
face of  the  moon,  and  for  preventing  its  being  wast- 
ed by  evaporation :  perhaps  it  remains  unaltered  in 
quantity,  imparting  to  the  lunar  regions  perpetual  ver- 
dure and  fertility."  To  this  I  reply,  that  the  bare  pos- 
sibility of  a  thing  is  but  slight  evidence  of  its  reality ; 
nor  is  such  a  condition  possible,  except  by  miracle.  If 
they  grant  that  the  laws  of  Nature  are  the  same  in  the 
moon  as  in  the  earth,  then,  according  to  the  foregoing 
reasoning,  there  cannot  be  water  in  the  moon ;  but  if 
they  say  that  the  laws  of  Nature  are  not  the  same  there 
as  here,  then  we  cannot  reason  at  all  respecting  them. 
One  who  resorts  to  a  subterfuge  of  this  kind  ruins  his 
own  cause.  He  argues  the  existence  of  water  in  the 
moon,  from  the  analogy  of  that  planet  to  this.  But  if 
the  laws  of  Nature  are  not  the  same  there  as  here,  what 
becomes  of  his  analogy?  A  liquid  substance  which 
would  not  evaporate  by  such  a  degree  of  solar  heat  as 
falls  on  the  moon,  which  would  not  evaporate  the  faster, 

15  L.  A.     4 


170  LETTERS  ON  ASTRONOMY. 

in  consequence  of  the  diminished  atmospheric  pressure 
which  prevails  there,  could  not  be  water,  for  it  would 
not  have  the  properties  of  water,  and  things  are  known 
by  their  properties.  Whenever  we  desert  the  cardinal 
principle  of  the  Newtonian  philosophy, — that  the  laws 
of  Nature  are  uniform  throughout  all  her  realms, — we 
wander  in  a  labyrinth ;  all  analogies  are  made  void  ; 
all  physical  reasonings  cease ;  and  imaginary  possibili- 
ties or  direct  miracles  take  the  place  of  legitimate  nat- 
ural causes. 

On  the  supposition  that  the  moon  is  inhabited,  the 
question  has  often  been  raised,  whether  we  may  hope 
that  our  telescopes  will  ever  be  so  much  improved,  and 
our  other  means  of  observation  so  much  augmented, 
that  we  shall  be  able  to  discover  either  the  lunar  inhab- 
itants or  any  of  their  works. 

The  improbability  of  our  ever  identifying  artificial 
structures  in  the  moon  may  be  inferred  from  the  fact, 
that  a  space  a  mile  in  diameter  is  the  least  space  that 
could  be  distinctly  seen.  Extensive  works  of  art,  as 
large  cities,  or  the  clearing  up  of  large  tracts  of  country 
for  settlement  or  tillage,  might  indeed  afford  some  vari- 
eties of  surface  ;  but  they  would  be  merely  varieties  of 
light  and  shade,  and  the  individual  objects  that  occa- 
sioned them  would  probably  never  be  recognised  by 
their  distinctive  characters.  Thus,  a  building  equal  to 
the  great  pyramid  of  Egypt,  which  covers  a  space  less 
than  the  fifth  of  a  mile  in  diameter,  would  not  be  dis- 
tinguished by  its  figure  ;  indeed,  it  would  be  a  mere 
point.  Still  less  is  it  probable  that  we  shall  ever  dis- 
cover any  inhabitants  in  the  moon.  Were  we  to  view 
the  moon  with  a  telescope  that  magnifies  ten  thousand 
times,  it  would  bring  the  moon  apparently  ten  thous- 
and times  nearer,  and  present  it  to  the  eye  like  a  body 
twenty-four  miles  off.  But  even  this  is  a  distance  too 
great  for  us  see  the  works  of  man  with  distinctness. 
Moreover,  from  the  nature  of  the  telescope  itself,  we 
can  never  hope  to  apply  a  magnifying  power  so  high 
as  that  here  supposed.  As  I  explained  to  you,  when 


THE  MOON.  171 

speaking  of  the  telescope,  whenever  we  increase  the 
magnifying  power  of  this  instrument  we  diminish  its 
field  of  view,  so  that  with  very  high  magnifiers  we  can 
see  nothing  but  a  point,  such  as  a  fixed  star.  We  at 
the  same  time,  also,  magnify  the  vapors  and  smoke  of 
the  atmosphere,  and  all  the  imperfections  of  the  me- 
dium, which  greatly  obscures  the  object,  and  prevents 
our  seeing  it  distinctly.  Hence  it  is  generally  most 
satisfactory  to  view  the  moon  with  low  powers,  which 
afford  a  large  field  of  view  and  give  a  clear  light. 
With  Clark's  telescope,  belonging  to  Yale  College,  we 
seldom  gain  any  thing  by  applying  to  the  moon  a  high- 
er power  than  one  hundred  and  eighty,  although  the 
instrument  admits  of  magnifiers  as  high  as  four  hundred 
and  fifty. 

Some  writers,  however,  suppose  that  possibly  we  may 
trace  indications  of  lunar  inhabitants  in  their  works,  and 
that  they  may  in  like  manner  recognise  the  existence 
of  the  inhabitants  of  our  planet.  An  author,  who  has 
reflected  much  on  subjects  of  this  kind,  reasons  as  fol- 
lows :  "A  navigator  who  approaches  within  a  certain 
distance  of  a  small  island,  although  he  perceives  no 
human  being  upon  it,  can  judge  with  certainty  that  it 
is  inhabited,  if  he  perceives  human  habitations,  villages, 
corn-fields,  or  other  traces  of  cultivation.  In  like  man- 
ner, if  we  could  perceive  changes  or  operations  in  the 
moon,  which  could  be  traced  to  the  agency  of  intelli- 
gent beings,  we  should  then  obtain  satisfactory  evi- 
dence that  such  beings  exist  on  that  planet ;  and  it  is 
thought  possible  that  such  operations  may  be  traced. 
A  telescope  which  magnifies  twelve  hundred  times  will 
enable  us  to  perceive,  as  a  visible  point  on  the  surface 
of  the  moon,  an  object  whose  diameter  is  only  about 
three  hundred  feet.  Such  an  object  is  not  larger  than 
many  of  our  public  edifices ;  and  therefore,  were  any 
such  edifices  rearing  in  the  moon,  or  were  a  town  or 
city  extending  its  boundaries,  or  were  operations  of  this 
description  carrying  on,  in  a  district  where  no  such 
edifices  had  previously  been  erected,  such  objects  and 


172  LETTERS  ON  ASTRONOMY. 

operations  might  probably  be  detected  by  a  minute  in- 
spection. Were  a  multitude  of  living  creatures  moving 
from  place  to  place,  in  a  body,  or  were  they  even  en- 
camping in  an  extensive  plain,  like  a  large  army,  or 
like  a  tribe  of  Arabs  in  the  desert,  and  afterwards  re- 
moving, it  is  possible  such  changes  might  be  traced  by 
the  difference  of  shade  or  color,  which  such  movements 
would  produce.  In  order  to  detect  such  minute  objects 
and  operations,  it  would  be  requisite  that  the  surface  of 
the  moon  should  be  distributed  among  at  least  a  hundred 
astronomers,  each  having  a  spot  or  two  allotted  to  him, 
as  the  object  of  his  more  particular  investigation,  and 
that  the  observations  be  continued  for  a  period  of  at 
least  thirty  or  forty  years,  during  which  time  certain 
changes  would  probably  be  perceived,  arising  either 
from  physical  causes,  or  from  the  operations  of  living 
agents."* 


LETTER  XVI. 


THE  MOON. PHASES. HARVEST  MOON. ITERATIONS. 

First  to  the  neighboring  Moon  this  mighty  key 
ilied.     Behold  !  it  turned 


The  secret  wards,  it  opened  wide  the  course 

And  various  aspects  of  the  queen  of  night  : 

Whether  she  wanes  into  a  scanty  orb, 

Or,  waxing  broad,  with  her  pale  shadowy  light, 

In  a  soft  deluge  overflows  the  sky." — Thomson's  Elegy. 

LET  us  now  inquire  into  the  revolutions  of  the  moon 
around  the  earth,  and  the  various  changes  she  under- 
goes every  month,  called  her  phases,  which  depend  on 
the  different  positions  she  assumes,  with  respect  to  the 
earth  and  the  sun,  in  the  course  of  her  revolution. 

The  moon  revolves  about  the  earth  from  west  to  east. 
Her  apparent  orbit,  as  traced  out  on  the  face  of  the 
sky,  is  a  great  circle ;  but  this  fact  would  not  certainly 
prove  that  the  orbit  is  really  a  circle,  since,  if  it  were 
an  ellipse,  or  even  a  more  irregular  curve,  the  projec- 

*  Dick's  '  Celestial  Scenery.' 


THE  MOON.  173 

tion  of  it  on  the  face  of  the  sky  would  be  a  circle,  as 
explained  to  you  before.  (See  page  148.)  The  moon 
is  comparatively  so  near  to  the  earth,  that  her  apparent 
movements  are  very  rapid,  so  that,  by  attentively  watch- 
ing her  progress  in  a  clear  night,  we  may  see  her  move 
from  star  to  star,  changing  her  place  perceptibly,  every 
few  hours.  The  interval  during  which  she  goes  through 
the  entire  circuit  of  the  heavens,  from  any  star  until 
she  comes  round  to  the  same  star  again,  is  called  a  si- 
dereal month,  and  consists  of  about  twenty-seven  and 
one  fourth  days.  The  time  which  intervenes  between 
one  new  moon  and  another  is  called  a  synodical  month, 
and  consists  of  nearly  twenty-nine  and  a  half  days.  A 
new  moon  occurs  when  the  sun  and  moon  meet  in  the 
same  part  of  the  heavens ;  but  the  sun  as  well  as  the 
moon  is  apparently  travelling  eastward,  and  nearly  at 
the  rate  of  one  degree  a  day,  and  consequently,  during 
the  twenty-seven  days  while  the  moon  has  been  going 
round  the  earth,  the  sun  has  been  going  forward  about 
the  same  number  of  degrees  in  the  same  direction. 
Hence,  when  the  moon  comes  round  to  the  part  of  the 
heavens  where  she  passed  the  sun  last,  she  does  not 
find  him  there,  but  must  go  on  more  than  two  days, 
before  she  comes  up  with  him  again. 

The  moon  does  not  pursue  precisely  the  same  track 
around  the  earth  as  the  sun  does,  in  his  apparent,  annual 
motion,  though  she  never  deviates  far  from  that  track. 
The  inclination  of  her  orbit  to  the  ecliptic  is  only  about 
five  degrees,  and  of  course  the  moon  is  never  seen  fur- 
ther from  the  ecliptic  than  about  that  distance,  and  she 
is  commonly  much  nearer  to  the  ecliptic  than  five  de- 
grees. We  may  therefore  see  nearly  what  is  the  situa- 
tion of  the  ecliptic  in  our  evening  sky  at  any  particu- 
lar time  of  year,  just  by  watching  the  path  which  the 
moon  pursues,  from  night  to  night,  from  new  to  full 
moon. 

The  two  points  where  the  moon's  orbit  crosses  the 
ecliptic  are  called  her  nodes.     They  are  the  intersections 
of  the  lunar  and  solar  orbits,  as  the  equinoxes  are  the 
15* 


174  LETTERS  ON  ASTRONOMY. 

intersections  of  the  equinoctial  and  ecliptic,  and,  like  the 
latter,  are  one  hundred  and  eighty  degrees  apart. 

The  changes  of  the  moon,  commonly  called  her 
phases,  arise  from  different  portions  of  her  illuminated 
side  being  turned  towards  the  earth  at  different  times. 
When  the  moon  is  first  seen  after  the  setting  sun,  her 
form  is  that  of  a  bright  crescent,  on  the  side  of  the 
disk  next  to  the  sun,  while  the  other  portions  of  the 
disk  shine  with  a  feeble  light,  reflected  to  the  moon 
from  the  earth.  Every  night,  we  observe  the  moon  to 
be  further  and  further  eastward  of  the  sun,  until,  when 
she  has  reached  an  elongation  from  the  sun  of  ninety  de- 
grees, half  her  visible  disk  is  enlightened,  and  she  is 
said  to  be  in  her  first  quarter.  The  terminator,  or 
line  which  separates  the  illuminated  from  the  dark 
part  of  the  moon,  is  convex  towards  the  sun  from  the 
new  to  the  first  quarter,  and  the  moon  is  said  to  be 
horned.  The  extremities  of  the  crescent  are  called 
cusps.  At  the  first  quarter,  the  terminator  becomes  a 
straight  line,  coinciding  with  the  diameter  of  the  disk ; 
but  after  passing  this  point,  the  terminator  becomes 
concave  towards  the  sun,  bounding  that  side  of  the 
moon  by  an  elliptical  curve,  when  the  moon  is  said  to 
be  gibbous.  When  the  moon  arrives  at  the  distance 
of  one  hundred  and  eighty  degrees  from  the  sun,  the 
entire  circle  is  illuminated,  and  the  moon  is  full.  She 
is  then  in  opposition  to  the  sun,  rising  about  the  time 
the  sun  sets.  For  a  week  after  the  full,  the  moon  ap- 
pears gibbous  again,  until,  having  arrived  within  ninety 
degrees  of  the  sun,  she  resumes  the  same  form  as  at  the 
first  quarter,  being  then  at  her  third  quarter.  From 
this  time  until  new  moon,  she  exhibits  again  the  form 
of  a  crescent  before  the  rising  sun,  until,  approaching 
her  conjunction  with  the  sun,  her  narrow  thread  of 
light  is  lost  in  the  solar  blaze ;  and  finally,  at  the  mo- 
ment of  passing  the  sun,  the  dark  side  is  wholly  turned 
towards  us,  and  for  some  time  we  lose  sight  of  the 
moon. 

By  inspecting  Fig,  38,  (where  T  represents  the  earth, 


PHASES   OF  THE  MOON. 
Fig.  38. 


175 


A,  B,  C,  &c.,  the  moon  in  her  orbit,  and  a,  b,  c,  &c., 
her  phases,  as  seen  in  the  heavens,)  we  shall  easily  see 
how  all  these  changes  occur. 

You  have  doubtless  observed,  that  the  moon  appears 
much  further  in  the  south  at  one  time  than  at  another, 
when  of  the  same  age.  This  is  owing  to  the  fact  that 
the  ecliptic,  and  of  course  the  moon's  path,  which  is 
always  very  near  it,  is  differently  situated  with  respect  to 
the  horizon,  at  a  given  time  of  night,  at  different  sea- 
sons of  the  year.  This  you  will  see  at  once,  by  turning 
to  an  artificial  globe,  and  observing  how  the  ecliptic 
stands  with  respect  to  the  horizon,  at  different  peri- 


176  LETTERS  ON  ASTRONOMY. 

ods  of  the  revolution.  Thus,  if  we  place  the  two  equi- 
noctial points  in  the  eastern  and  western  horizon,  Libra 
being  in  the  west,  it  will  represent  the  position  of  the 
ecliptic  at  sunset  in  the  month  of  September,  when  the 
sun  is  crossing  the  equator ;  and  at  that  season  of  the 
year,  the  moon's  path  through  our  evening  sky,  one 
evening  after  another,  from  new  to  full,  will  be  nearly 
along  the  same  route,  crossing  the  meridian  nearly  at 
right  angles.  But  if  we  place  the  Winter  solstice,  or 
first  degree  of  Capricorn,  in  the  western  horizon,  and 
the  first  degree  of  Cancer  in  the  eastern,  then  the  po- 
sition of  the  ecliptic  will  be  very  oblique  to  the  meridi- 
an, the  Winter  solstice  being  very  far  in  the  southwest, 
and  the  Summer  solstice  very  far  in  the  northeast ;  and 
the  course  of  the  moon  from  new  to  full  will  be  nearly 
along  this  track.  Keeping  these  things  in  mind,  we 
may  easily  see  why  the  moon  runs  sometimes  high  and 
sometimes  low.  Recollect,  also,  that  the  new  moon  is 
always  in  the  same  part  of  the  heavens  with  the  sun, 
and  that  the  full  moon  is  in  the  opposite  part  of  the 
heavens  from  the  sun.  Now,  when  the  sun  is  at  the 
Winter  solstice,  it  sets  far  in  the  southwest,  and  accord- 
ingly the  new  moon  runs  very  low ;  but  the  full  moon, 
being  in  the  opposite  tropic,  which  rises  far  in  the 
northeast,  runs  very  high,  as  is  known  to  be  the  case  in 
mid-winter.  But  now  take  the  position  of  the  ecliptic 
in  mid-summer.  Then,  at  sunset,  the  tropic  of  Cancer 
is  in  the  northwest,  and  the  tropic  of  Capricorn  in  the 
southeast ;  consequently,  the  new  moons  run  high  and 
the  full  moons  low. 

It  is  a  natural  consequence  of  this  arrangement,  to 
render  the  moon's  light  the  most  beneficial  to  us,  by 
giving  it  to  us  in  greatest  abundance,  when  we  have 
least  of  the  sun's  light,  and  giving  it  to  us  most  spar- 
ingly, when  the  sun's  light  is  greatest.  Thus,  during 
the  long  nights  of  Winter,  the  full  moon  runs  high, 
and  continues  a  very  long  time  above  the  horizon ; 
while  in  mid-summer,  the  full  moon  runs  low,  and  is 
above  the  horizon  for  a  much  shorter  period.  This  ar- 


HARVEST  MOON.  177 

rangement  operates  very  favorably  to  the  inhabitants  of 
the  polar  regions.  At  the  season  when  the  sun  is  ab- 
sent, and  they  have  constant  night,  then  the  moon, 
during  the  second  and  third  quarters,  embracing  the 
season  of  full  moon,  is  continually  above  the  horizon, 
compensating  in  no  small  degree  for  the  absence  of  the 
sun ;  while,  during  the  Summer  months,  when  the  sun 
is  constantly  above  the  horizon,  and  the  light  of  the 
moon  is  not  needed,  then  she  is  above  the  horizon  dur- 
ing the  first  and  last  quarters,  when  her  light  is  least, 
affording  at  that  time  her  greatest  light  to  the  inhabi- 
tants of  the  other  hemisphere,  from  whom  the  sun  is 
withdrawn. 

About  the  time  of  the  Autumnal  equinox,  the  moon, 
when  near  her  full,  rises  about  sunset  a  number  of 
nights  in  succession.  This  occasions  a  remarkable 
number  of  brilliant  moonlight  evenings ;  and  as  this 
is,  in  England,  the  period  of  harvest,  the  phenomenon 
is  called  the  harvest  moon.  Its  return  is  celebrated, 
particularly  among  the  peasantry,  by  festive  dances,  and 
kept  as  a  festival,  called  the  harvest  home, — an  occasion 
often  alluded  to  by  the  British  poets.  Thus  Henry 
Kirke  White: 

"  Moon  of  harvest,  herald  mild 
Of  plenty,  rustic  labor's  child, 
Hail,  O  hail  !  1  greet  thy  beam, 
As  soft  it  trembles  o'er  the  stream, 
And  gilds  the  straw-thatch'd  hamlet  wide, 
Where  innocence  and  peace  reside  ; 
'Tis  thou  that  glad'st  with  joy  the  rustic  throng, 
Promptest  the  tripping  dance,  th'  exhilarating  song." 

To  understand  the  reason  of  the  harvest  moon,  we 
will,  as  before,  consider  the  moon's  orbit  as  coinciding 
with  the  ecliptic,  because  we  may  then  take  the  eclip- 
tic, as  it  is  drawn  on  the  artificial  globe,  to  represent 
that  orbit.  We  will  also  bear  in  mind,  (what  has  been 
fully  illustrated  under  the  last  head,)  that,  since  the 
ecliptic  cuts  the  meridian  obliquely,  while  all  the  cir- 
cles of  diurnal  revolution  cut  it  perpendicularly,  differ- 
ent portions  of  the  ecliptic  will  cut  the  horizon  at  dif- 


178  LETTERS   ON  ASTRONOMY. 

ferent  angles.  Thus,  when  the  equinoxes  are  in  the 
horizon,  the  ecliptic  makes  a  very  small  angle  with  the 
horizon ;  whereas,  when  the  solstitial  points  are  in  the 
horizon,  the  same  angle  is  far  greater.  In  the  former 
case,  a  body  moving  eastward  in  the  ecliptic,  and  being 
at  the  eastern  horizon  at  sunset,  would  descend  but  a 
little  way  below  the  horizon  in  moving  over  many  de- 
grees of  the  ecliptic.  Now,  this  is  just  the  case  of  the 
moon  at  the  time  of  the  harvest  home,  about  the  time 
of  the  Autumnal  equinox.  The  sun  being  then  in  Li- 
bra, and  the  moon,  when  full,  being  of  course  opposite 
to  the  sun,  or  in  Aries ;  and  moving  eastward,  in  or 
near  the  ecliptic,  at  the  rate  of  about  thirteen  degrees 
per  day,  would  descend  but  a  small  distance  below  the 
horizon  for  five  or  six  days  in  succession  ;  that  is  for 
two  or  three  days  before,  and  the  same  number  of  days 
after,  the  full ;  and  would  consequently  rise  during  all 
these  evenings  nearly  at  the  same  time,  namely,  a  little 
before,  or  a  little  after,  sunset,  so  as  to  afford  a  remark- 
able succession  of  fine  moonlight  evenings. 

The  moon  turns  on  her  axis  in  the  same  time  in 
which  she  revolves  around  the  earth.  This  is  known 
by  the  moon's  always  keeping  nearly  the  same  face  to- 
wards us,  as  is  indicated  by  the  telescope,  which  could 
not  happen  unless  her  revolution  on  her  axis  kept  pace 
with  her  motion  in  her  orbit.  Take  an  apple,  to  rep- 
resent the  moon ;  stick  a  knittingneedle  through  it,  in 
the  direction  of  the  stem,  to  represent  the  axis,  in  which 
case  the  two  eyes  of  the  apple  will  aptly  represent  the 
poles.  Through  the  poles  cut  a  line  around  the  apple, 
dividing  it  into  two  hemispheres,  and  mark  them,  so 
as  to  be  readily  distinguished  from  each  other.  Now 
place  a  candle  on  the  table,  to  represent  the  earth,  and 
holding  the  apple  by  the  knittingneedle,  carry  it  round 
the  candle,  and  you  will  see  that,  unless  you  make  the 
apple  turn  round  on  the  axis  as  you  carry  it  about  the 
candle,  it  will  present  different  sides  towards  the  can- 
dle ;  and  that,  in  order  to  make  it  always  present  the 
same  side,  it  will  be  necessary  to  make  it  revolve  ex- 


LIBRATIONS.  179 

actly  once  on  its  axis,  while  it  is  going  round  the  circle, 
— the  revolution  on  its  axis  always  keeping  exact  pace 
with  the  motion  in  its  orbit.  The  same  thing  will  be 
observed,  if  you  walk  around  a  tree,  always  keeping 
your  face  towards  the  tree.  If  you  have  your  face  to- 
wards the  tree  when  you  set  out,  and  walk  round  with- 
out turning,  when  you  have  reached  the  opposite  side 
of  the  tree,  your  back  will  be  towards  it,  and  you  will 
find  that,  in  order  to  keep  your  face  constantly  towards 
the  tree,  it  will  be  necessary  to  turn  yourself  round  on 
your  heel  at  the  same  rate  as  you  go  forward. 

Since,  however,  the  motion  of  the  moon  on  its  axis 
is  uniform,  while  the  motion  in  its  orbit  is  unequal,  the 
moon  does  in  fact  reveal  to  us  a  little  sometimes  of  one 
side  and  sometimes  of  the  other.  Thus  if,  while  car- 
rying the  apple  round  the  candle,  you  carry  it  forward 
a  little  faster  than  the  rate  at  which  it  turns  on  its 
axis,  a  portion  of  the  hemisphere  usually  out  of  sight  is 
brought  into  view  on  one  side  ;  or  if  the  apple  is  moved 
forward  slower  than  it  is  turned  on  its  axis,  a  portion 
of  the  same  hemisphere  comes  into  view  on  the  other 
side.  These  appearances  are  called  the  moon's  libra- 
tions  in  longitude.  .The  moon  has  also  a  libration  in 
latitude ; — so  called,  because  in  one  part  of  her  revolu- 
tion more  of  the  region  around  one  of  the  poles  comes 
into  view,  and,  in  another  part  of  the  revolution,  more  of 
the  region  around  the  other  pole,  which  gives  the  ap- 
pearance of  a  tilting  motion  to  the  moon's  axis.  This 
is  owing  to  the  fact,  that  the  moon's  axis  is  inclined  to 
the  plane  of  her  orbit.  If,  in  the  experiment  with  the 
apple,  you  hold  the  knittingneedle  parallel  to  the  can- 
dle, (in  which  case  the  axis  will  be  perpendicular  to 
the  plane  of  revolution,)  the  candle  will  shine  upon 
both  poles  during  the  whole  circuit,  and  an  eye  situated 
where  the  candle  is  would  constantly  see  both  poles ; 
but  now  incline  the  needle  towards  the  plane  of  revo- 
lution, and  carry  it  round,  always  keeping  it  parallel  to 
itself,  and  you  will  observe  that  the  two  poles  will  be 
alternately  in  and  out  of  sight. 


180  LETTERS  ON  ASTRONOMY. 

The  moon  exhibits  another  appearance  of  this  kind, 
called  her  diurnal  libration,  depending  on  the  daily 
rotation  of  the  spectator.  She  turns  the  same  face  to- 
wards the  centre  of  the  earth  only,  whereas  we  view 
her  from  the  surface.  When  she  is  on  the  meridian, 
we  view  her  disk  nearly  as  though  we  viewed  it  from 
the  centre  of  the  earth,  and  hence,  in  this  situation, 
it  is  subject  to  little  change ;  but  when  she  is  near 
the  horizon,  our  circle  of  vision  takes  in  more  of  the 
upper  limb  than  would  be  presented  to  a  spectator  at 
the  centre  of  the  earth.  Hence,  from  this  cause,  we  see 
a  portion  of  one  limb  while  the  moon  is  rising,  which 
is  gradually  lost  sight  of,  and  we  see  a  portion  of  the 
opposite  limb,  as  the  moon  declines  to  the  west.  You 
will  remark  that  neither  of  the  foregoing  changes  im- 
plies any  actual  motion  in  the  moon,  but  that  each 
arises  from  a  change  of  position  in  the  spectator.  Since 
the  succession  of  day  and  night  depends  on  the  revolu- 
tion of  a  planet  on  its  own  axis,  and  it  takes  the  moon 
twenty-nine  and  a  half  days  to  perform  this  revolution, 
so  that  the  sun  shall  go  from  the  meridian  of  any  place 
and  return  to  the  same  meridian  again,  of  course  the 
lunar  day  occupies  this  long  period.  So  protracted  an 
exposure  to  the  sun's  rays,  especiallv  in  the  equatorial 
regions  of  the  moon,  must  occasion  n  excessive  accu- 
mulation of  heat ;  and  so  long  an  aosence  of  the  sun 
must  occasion  a  corresponding  degree  of  cold.  A  spec- 
$or  on  the  side  of  the  moon  which  is  opposite  to  us 
>uld  never  see  ^  earth,  but  one  on  the  side  next  to 
us  would  see  the  earth  constantly  in  his  firmament,  un- 
dergoing a  gradual  succession  of  changes,  corresponding 
to  those  which  the  moon  exhibits  to  the  earth,  but  in 
the  reverse  order.  Thus,  when  it  is  full  moon  to  us, 
the  earth,  as  seen  from  the  moon,  is  then  in  conjunction 
the  sun,  and  of  course  presents  her  dark  side  to 

ooon  after  this,  an  inhabitant  of  the  moon  would 
see  a  crescent,  resembling  our  new  moon,  which  would 
in  like  manner  increase  and  go  through  all  the  changes, 


ITERATIONS.  181 

from  new  to  full,  and  from  full  to  new,  as  we  see  them 
in  the  moon.  There  are,  however,  in  the  two  cases, 
several  striking  points  of  difference.  In  the  first  place, 
instead  of  twenty-nine  and  a  half  days,  all  these 
changes  occur  in  one  lunar  day  and  night.  During  the 
first  and  last  quarters,  the  changes  would  occur  in  the 
day-time  ;  but  during  the  second  and  third  quarters, 
during  the  night.  By  this  arrangement,  the  lunarians 
would  enjoy  the  greatest  possible  benefit  from  the  light 
afforded  by  the  earth,  since  in  the  half  of  her  revolu- 
tion where  she  appears  to  them  as  full,  she  would  be 
present  while  the  sun  was  absent,  and  would  afford 
her  least  light  while  the  sun  was  present.  In  the  sec- 
ond place,  the  earth  would  appear  thirteen  times  as 
large  to  a  spectator  on  the  moon  as  the  moon  appears 
to  us,  and  would  afford  nearly  the  same  proportion  of 
light,  so  that  their  long  nights  must  be  continually 
cheered  by  an  extraordinary  degree  of  light  derived  from 
this  source  ;  and  if  the  full  moon  is  hailed  by  our  poets 
as  "  refulgent  lamp  of  night,"*  with  how  much  more 
reason  might  a  lunarian  exult  thus,  in  view  of  the  splen- 
did orb  that  adorns  his  nocturnal  sky !  In  the  third 
place,  the  earth,  as  viewed  from  any  particular  place 
on  the  moon,  would  occupy  invariably  the  same  part  of 
the  heavens.  F*'  while  the  rotation  of  the  moon  on 
her  axis  from  west  to  east  would  appear  to  make  th^ 
earth  (as  the  moon  does  to  us)  revolve  from  east  to 
west,  the  corresponding  progress  of  the  moon  in  h  '- 

*  "  As  when  the  moon,  refulgent  lamp  of  night, 

O'er  heaven's  clear  azure  sheds  her  sacred  light,  ,^^f 

When  not  a  breath  disturbs  the  deep  serene, 

And  not  a  cloud  o'ercasts  the  solemn  scene, 

Around  her  throne  the  vivid  planets  roll, 

And  stars  unnumbered  jrild  the 

O'er  the  dark  trees  a  yellower 

And  tip  with  silver  every  moi:  •  id  ; 

Then  shine  the  vales,  :  '  rise, 

A  flood  of  glory  hursts  from  all  iliu  skies  ; 

The  conscious  swains,  rejoicing  in  the  sight, 

Eye  the  blue  vault,  and  bless  the  useful  light." 

Pope's  Homer. 
16  L.  A. 


182  LETTERS   ON  ASTRONOMY. 

orbit  would  make  the  earth  appear  to  revolve  from  west 
to  east ;  and  as  these  two  motions  are  equal,  their  unit- 
ed effect  would  be  to  keep  the  moon  apparently  stationa- 
ry in  the  sky.  Thus,  a  spectator  at  E,  Fig.  38,  page  175, 
in  the  middle  of  the  disk  that  is  turned  towards  the  earth, 
would  have  the  earth  constantly  on  his  meridian,  and 
at  E,  the  conjunction  of  the  earth  and  sun  would 
occur  at  mid-day ;  but  when  the  moon  arrived  at  G, 
the  same  place  would  be  on  the  margin  of  the  circle 
of  illumination,  and  will  have  the  sun  in  the  horizon ; 
but  the  earth  would  still  be  on  his  meridian  and  in 
quadrature.  In  like  manner,  a  place  situated  on  the 
margin  of  the  circle  of  illumination,  when  the  moon  is 
at  E,  would  have  the  earth  in  the  horizon  ;  and  the 
same  place  would  always  see  the  earth  in  the  hori- 
zon, except  the  slight  variations  that  would  occur  from 
the  librations  of  the  moon.  In  the  fourth  place,  the 
earth  would  present  to  a  spectator  on  the  moon  none 
of  that  uniformity  of  aspect  which  the  moon  presents 
to  us,  but  would  exhibit  an  appearance  exceedingly 
diversified.  The  comparatively  rapid  rotation  of  the 
earth,  repeated  fifteen  times  during  a  lunar  night,  would 
present,  in  rapid  succession,  a  view  of  our  seas,  oceans, 
continents,  and  mountains,  all  diversified  by  our  clouds, 
storms,  and  volcanoes. 


LETTER  XVII. 

MOON'S  ORBIT. HER  IRREGULARITIES. 

u  Some  say  the  zodiac  constellations 
Have  long  since  left  their  antique  stations, 
Above  a  sign,  and  prove  the  same 
In  Taurus  now,  once  in  the  Ram  ; 
That  in  twelve  hundred  years  and  odd, 
The  sun  has  left  his  ancient  road, 
And  nearer  to  the  earth  is  come, 
'Bove  fifty  thousand  miles  from  home." — Hudibras. 

WE  have  thus  far  contemplated  the  revolution  of  the 
moon  around  the  earth  as  though  the  earth  were  at 


183 

rest.  But  in  order  to  have  just  ideas  respecting  the 
moon's  motions,  we  must  recollect  that  the  moon  like- 
wise revolves  along  with  the  earth  around  the  sun.  It 
is  sometimes  said  that  the  earth  carries  the  moon  along 
with  her,  in  her  annual  revolution.  This  language 
may  convey  an  erroneous  idea ;  for  the  moon,  as  well 
as  the  earth,  revolves  around  the  sun  under  the  in- 
fluence of  two  forces,  which  are  independent  of  the 
earth,  and  would  continue  her  motion  around  the  sun, 
were  the  earth  removed  out  of  the  way.  Indeed,  the 
moon  is  attracted  towards  the  sun  two  and  one  fifth 
times  more  than  towards  the  earth,  and  would  abandon 
the  earth,  were  not  the  latter  also  carried  along  with 
her  by  the  same  forces.  So  far  as  the  sun  acts  equally 
on  both  bodies,  the  motion  with  respect  to  each  other 
would  not  be  disturbed.  Because  the  gravity  of  the 
moon  towards  the  sun  is  found  to  be  greater,  at  the 
conjunction,  than  her  gravity  towards  the  earth,  some 
have  apprehended  that,  if  the  doctrine  of  universal  grav- 
itation is  true,  the  moon  ought  necessarily  to  abandon 
the  earth.  In  order  to  understand  the  reason  why  it 
does  not  do  thus,  we  must  reflect,  that,  when  a  body  is 
revolving  in  its  orbit  under  the  influence  of  the  pro- 
jectile force  and  gravity,  whatever  diminishes  the  force 
of  gravity,  while  that  of  projection  remains  the  same, 
causes  the  body  to  approach  nearer  to  the  tangent  of 
her  orbit,  and  of  course  to  recede  from  the  centre ;  and 
whatever  increases  the  amount  of  gravity,  carries  the 
body  towards  the  centre.  Thus,  in  Fig.  33,  page  152, 
if,  with  a  certain  force  of  projection  acting  in  the  direc- 
tion A  B,  and  of  attraction,  in  the  direction  A  C,  the 
attraction  which  caused  a  body  to  move  in  the  line 
A  D  were  diminished,  it  would  move  nearer  to  the  tan- 
gent, as  in  A  E,  or  A  F.  Now,  when  the  moon  is  in 
conjunction,  her  gravity  towards  the  earth  acts  in  oppo- 
sition to  that  towards  the  sun,  (see  Fig.  38,  page  175,} 
while  her  velocity  remains  too  great  to  carry  her  with 
what  force  remains,  in  a  circle  about  the  sun,  and  she 
therefore  recedes  from  the  sun,  and  commences  her 


184  LETTERS  ON  ASTRONOMY. 

revolution  around  the  earth.  On  arriving  at  the  oppo- 
sition, the  gravity  of  the  earth  conspires  with  that  of 
the  sun,  and  the  moon's  projectile  force  being  less  than 
that  required  to  make  her  revolve  in  a  circular  orbit, 
when  attracted  towards  the  sun  by  the  sum  of  these 
forces,  she  accordingly  begins  to  approach  the  sun,  and 
descends  again  to  the  conjunction. 

The  attraction  of  the  sun,  however,  being  every  where 
greater  than  that  of  the  earth,  the  actual  path  of  the 
moon  around  the  sun  is  every  where  concave  towards 
the  latter.  Still,  the  elliptical  path  of  the  moon  around 
the  earth  is  to  be  conceived  of,  in  the  same  way  as 
though  both  bodies  were  at  rest  with  respect  to  the  sun. 
Thus,  while  a  steam-boat  is  passing  swiftly  around  an 
island,  and  a  man  is  walking  slowly  around  a  post  in 
the  cabin,  the  line  which  he  describes  in  space  between 
the  forward  motion  of  the  boat  and  his  circular  motion 
around  the  post,  may  be  every  where  concave  towards 
the  island,  while  his  path  around  the  post  will  still  be 
the  same  as  though  both  were  at  rest.  A  nail  in  the 
rim  of  a  coach-wheel  will  turn  around  the  axis  of  the 
wheel,  when  the  coach  has  a  forward  motion,  in  the 
same  manner  as  when  the  coach  is  at  rest,  although  the 
line  actually  described  by  the  nail  will  be  the  resultant 
of  both  motions,  and  very  different  from  either. 

We  have  hitherto  regarded  the  moon  as  describing 
a  great  circle  on  the  face  of  the  sky,  such  being  the 
visible  orbit,  as  seen  by  projection.  But,  on  a  more 
exact  investigation,  it  is  found  that  her  orbit  is  not  a 
circle,  and  that  her  motions  are  subject  to  very  numer- 
ous irregularities.  These  will  be  best  understood  in 
connexion  with  the  causes  on  which  they  depend.  The 
law  of  universal  gravitation  has  been  applied  with  won- 
derful success  to  their  developement,  and  its  results  have 
conspired  with  those  of  long-continued  observation,  to 
furnish  the  means  of  ascertaining  with  great  exactness 
the  place  of  the  moon  in  the  heavens,  at  any  given  in- 
stant of  time,  past  or  future,  and  thus  to  enable  astron- 
omers to  determine  longitudes,  to  calculate  eclipses. 


185 

and  to  solve  other  problems  of  the  highest  interest. 
The  whole  number  of  irregularities  to  which  the  moon 
is  subject  is  not  less  than  sixty,  but  the  greater  part 
are  so  small  as  to  be  hardly  deserving  of  attention  ;  but 
as  many  -as  thirty  require  to  be  estimated  and  allow- 
ed for,  before  we  can  ascertain  the  exact  place  of  the 
moon  at  any  given  time.  You  will  be  able  to  under- 
stand something  of  the  cause  of  these  irregularities,  if 
you  first  gain  a  distinct  idea  of  the  mutual  actions  of  the 
sun,  the  moon,  and  the  earth.  The  irregularities  in  the 
moon's  motions  are  due  chiefly  to  the  disturbing  influ- 
ence of  the  sun,  which  operates  in  two  ways ;  first,  by 
acting  unequally  on  the  earth  and  moon  ;  and  secondly, 
by  acting  obliquely  on  the  moon,  on  account  of  the  in- 
clination of  her  orbit  to  the  ecliptic.  If  the  sun  acted 
equally  on  the  earth  and  moon,  and  always  in  parallel 
lines,  this  action  would  serve  only  to  restrain  them  in 
their  annual  motions  around  the  sun,  and  would  not 
affect  their  actions  on  each  other,  or  their  motions 
about  their  common  centre  of  gravity.  In  that  case,  if 
they  were  allowed  to  fall  towards  the  sun,  they  would 
fall  equally,  and  their  respective  situations  would  not 
be  affected  by  their  descending  equally  towards  it. 
But,  because  the  moon  is  nearer  the  sun  in  one  half  of 
her  orbit  than  the  earth  is,  and  in  the  other  half  of  her 
orbit  is  at  a  greater  distance  than  the  earth  from  the 
sun,  while  the  power  of  gravity  is  always  greater  at  a 
less  distance ;  it  follows,  that  in  one  half  of  her  orbit 
the  moon  is  more  attracted  than  the  earth  towards  the 
sun,  and,  in  the  other  half,  less  attracted  than  the  earth. 
To  see  the  effects  of  this  process,  let  us  suppose  that  the 
projectile  motions  of  the  earth  and  moon  were  destroy- 
ed, and  that  they  were  allowed  to  fall  freely  towards 
the  sun.  (See  Fig.  38,  page  175.)  If  the  moon  was  in 
conjunction  with  the  sun,  or  in  that  part  of  her  orbit 
which  is  nearest  to  him,  the  moon  would  be  more  attract- 
ed than  the  earth,  and  fall  with  greater  velocity  towards 
the  sun ;  so  that  the  distance  of  the  moon  from  the 
earth  would  be  increased  by  the  fall.  If  the  moon  was 
16* 


186  LETTERS  ON  ASTRONOMY. 

in  opposition,  or  in  the  part  of  her  orbit  which  is  furthest 
from  the  sun,  she  would  be  less  attracted  than  the  earth 
by  the  sun,  and  would  fall  with  a  less  velocity,  and  be 
left  behind  ;  so  that  the  distance  of  the  moon  from  the 
earth  would  be  increased  in  this  case,  also.  If  the 
moon  was  in  one  of  the  quarters,  then  the  earth  and 
the  moon  being  both  attracted  towards  the  centre  of 
the  sun,  they  would  both  descend  directly  towards  that 
centre,  and,  by  approaching  it,  they  would  necessarily 
at  the  same  time  approach  each  other,  and  in  this  case 
their  distance  from  each  other  would  be  diminished. 
Now,  whenever  the  action  of  the  sun  would  increase 
their  distance,  if  they  were  allowed  to  fall  towards  the 
sun,  then  the  sun's  action,  by  endeavoring  to  separate 
them,  diminishes  their  gravity  to  each  other  ;  whenever 
the  sun's  action  would  diminish  the  distance,  then  it  in- 
creases their  mutual  gravitation.  Hence,  in  the  con- 
junction and  opposition,  their  gravity  towards  each  oth- 
er is  diminished  by  the  action  of  the  sun,  while  in  the 
quadratures  it  is  increased.  But  it  must  be  remem- 
bered, that  it  is  not  the  total  action  of  the  sun  on  them 
that  disturbs  their  motions,  but  only  that  part  of  it  which 
tends  at  one  time  to  separate  them,  and  at  another 
time  to  bring  them  nearer  together.  The  other  and 
far  greater  part  has  no  other  effect  than  to  retain  them 
in  their  annual  course  around  the  sun. 

The  cause  of  the  lunar  irregularities  was  first  investi- 
gated by  Sir  Isaac  Newton,  in  conformity  with  his  doc- 
trine of  universal  gravitation,  and  the  explanation  was 
first  published  in  the  c  Principia  ;'  but,  as  it  was  given  in 
a  mathematical  dress,  there  were  at  that  age  very  few 
persons  capable  of  reading  or  understanding  it.  Sev- 
eral eminent  individuals,  therefore,  undertook  to  give  a 
popular  explanation  of  these  difficult  points.  Among 
Newton's  contemporaries,  the  best  commentator  was 
M'Laurin,  a  Scottish  astronomer,  who  published  a  large 
work  entitled  '  M'Laurin's  Account  of  Sir  Isaac  New- 
ton's Discoveries.'  No  writer  of  his  own  day,  and,  in  my 
opinion,  no  later  commentator,  has  equalled  M'Laurin, 


187 

in  reducing  to  common  apprehension  the  leading  prin- 
ciples of  the  doctrine  of  gravitation,  and  the  explana- 
tion it  affords  of  the  motions  of  the  heavenly  bodies. 
To  this  writer  I  am  indebted  for  the  preceding  easy 
explanation  of  the  irregularities  of  the  moon's  motions, 
as  well  as  for  several  other  illustrations  of  the  same  sub- 
lime doctrine. 

The  figure  of  the  moon's  orbit  is  an  ellipse.  We  have 
before  seen,  that  the  earth's  orbit  around  the  sun  is  of 
the  same  figure ;  and  we  shall  hereafter  see  this  to  be 
true  of  all  the  planetary  orbits.  The  path  of  the  earth, 
however,  departs  very  little  from  a  circle ;  that  of  the 
moon  differs  materially  from  a  circle,  being  considera- 
bly longer  one  way  than  the  other.  Were  the  orbit  a 
circle  having  the  earth  in  the  centre,  then  the  radius 
vector,  or  line  drawn  from  the  centre  of  the  moon  to 
the  centre  of  the  earth,  would  always  be  of  the  same 
length ;  but  it  is  found  that  the  length  of  the  radius 
vector  is  only  fifty-six  times  the  radius  of  the  earth  when 
the  moon  is  nearest  to  us,  while  it  is  sixty-four  times  that 
radius  when  the  moon  is  furthest  from  us.  The  point 
in  the  moon's  orbit  nearest  the  earth  is  called  her  peri- 
gee ;  the  point  furthest  from  the  earth,  her  apogee.  We 
always  know  when  the  moon  is  at  one  of  these  points, 
by  her  apparent  diameter  or  apparent  velocity ;  for, 
when  at  the  perigee,  her  diameter  is  greater  than  at  any 
time,  and  her  motion  most  rapid ;  and,  on  the  other 
hand,  her  diameter  is  least,  and  her  motion  slowest, 
when  she  is  at  her  apogee. 

The  moon's  nodes  constantly  shift  their  positions 
in  the  ecliptic,  from  east  to  west,  at  the  rate  of  about 
nineteen  and  a  half  degrees  every  year,  returning  to 
the  same  points  once  in  eighteen  and  a  half  years.  In 
order  to  understand  what  is  meant  by  this  backward 
motion  of  the  nodes,  you  must  have  very  distinctly  in 
mind  the  meaning  of  the  terms  themselves  ;  and  if,  at 
any  time,  you  should  be  at  a  loss  about  the  signification 
of  any  word  that  is  used  in  expressing  an  astronomical 
proposition.  I  would  advise  you  to  turn  back  to  the  pre- 


188  LETTERS  ON  ASTRONOMY. 

vious  definition  of  that  term,  and  revive  its  meaning 
clearly  in  the  mind,  before  you  proceed  any  further. 
In  the  present  case,  you  will  recollect  that  the  moon's 
nodes  are  the  two  points  where  her  orbit  cuts  the 
plane  of  the  ecliptic.  Suppose  the  great  circle  of  the 
ecliptic  marked  out  on  the  face  of  the  sky  in  a  distinct 
line,  and  let  us  observe,  at  any  given  time,  the  exact 
moment  when  the  moon  crosses  this  line,  which  we  will 
suppose  to  be  close  to  a  certain  star ;  then,  on  its  next 
return  to  that  part  of  the  heavens,  we  shall  find  that  u 
crosses  the  ecliptic  sensibly  to  the  westward  of  that 
star,  and  so  on,  further  and  further  to  the  westward, 
every  time  it  crosses  the  ecliptic  at  either  node.  This 
fact  is  expressed  by  saying  that  the  nodes  retrograde 
on  the  ecliptic;  since  any  motion  from  east  to  west, 
being  contrary  to  the  order  of  the  signs,  is  called  retro- 
grade. The  line  which  joins  these  two  points,  or  the 
line  of  the  nodes,  is  also  said  to  have  a  retrograde  mo- 
tion, or  to  revolve  from  east  to  west  once  in  eighteen 
and  a  half  years. 

The  line  of  the  apsides  of  the  moon's  orbit  revolves 
from  west  to  east,  through  her  whole  course,  in  about 
nine  years.  You  will  recollect  that  the  apsides  of  an 
elliptical  orbit  are  the  two  extremities  of  the  longer  axis 
of  the  ellipse  ;  corresponding  to  the  perihelion  and  aphe- 
lion of  bodies  revolving  about  the  sun,  or  to  the  peri- 
gee and  apogee  of  a  body  revolving  about  the  earth. 
If,  in  any  revolution  of  the  moon,  we  should  accu- 
rately mark  the  place  in  the  heavens  where  the  moon  is 
nearest  the  earth,  (which  may  be  known  by  the  moon's 
apparent  diameter  being  then  greatest,)  we  should  find 
that,  at  the  next  revolution,  it  would  come  to  its  peri- 
gee a  little  further  eastward  than  before,  and  so  on,  at 
every  revolution,  until,  after  nine  years,  it  would  come 
to  its  perigee  nearly  at  the  same  point  as  at  first.  This 
fact  is  expressed  by  saying,  that  the  perigee,  and  of 
course  the  apogee,  revolves,  and  that  the  line  which 
joins  these  two  points,  or  the  line  of  the  apsides,  also 
revolves. 


MOON'S   IRREGULARITIES.  189 

These  are  only  a  few  of  the  irregularities  that  attend 
the  motions  of  the  moon.  These  and  a  few  others 
were  first  discovered  by  actual  observation  and  have 
been  long  known ;  but  a  far  greater  number  of  lunar 
irregularities  have  been  made  known  by  following  out 
all  the  consequences  of  the  law  of  universal  gravitation. 

The  moon  may  be  regarded  as  a  body  endeavoring 
to  make  its  way  around  the  earth,  but  as  subject  to  be 
continually  impeded,  or  diverted  from  its  main  course, 
'  y  the  action  of  the  sun  and  of  the  earth ;  sometimes 
acting  in  concert  and  sometimes  in  opposition  to  each 
other.  Now,  by  exactly  estimating  the  amount  of  these 
respective  forces,  and  ascertaining  their  resultant  or 
combined  effect,  in  any  given  case,  the  direction  and 
velocity  of  the  moon's  motion  may  be  accurately  deter- 
mined. But  to  do  this  has  required  the  highest  pow- 
ers of  the  human  mind,  aided  by  all  the  wonderful 
resources  of  mathematics.  Yet,  so  consistent  is  truth 
with  itself,  that,  where  some  minute  inequality  in  the 
moon's  motions  is  developed  at  the  end  of  a  long  and 
intricate  mathematical  process,  it  invariably  happens, 
that,  on  pointing  the  telescope  to  the  moon,  and  watch- 
ing its  progress  through  the  skies,  we  may  actually  see 
her  commit  the  same  irregularities,  unless  (as  is  the 
case  with  many  of  them)  they  are  too  minute  to  be 
matters  of  observation,  being  beyond  the  powers  of  our 
vision,  even  when  aided  by  the  best  telescopes.  But 
the  truth  of  the  law  of  gravitation,  and  of  the  results 
it  gives,  when  followed  out  by  a  chain  of  mathematical 
reasoning,  is  fully  confirmed,  even  in  these  minutest 
matters,  by  the  fact  that  the  moon's  place  in  the 
heavens,  when  thus  determined,  always  corresponds, 
with  wonderful  exactness,  to  the  place  which  she  is  ac- 
tually observed  to  occupy  at  that  time. 

The  mind,  that  was  first  able  to  elicit  from  the  opera- 
tions of  Nature  the  law  of  universal  gravitation,  and  af- 
terwards to  apply  it  to  the  complete  explanation  of  all 
the  irregular  wanderings  of  the  moon,  must  have  giv- 
en evidence  of  intellectual  powers  far  elevated  above 


190  LETTERS  ON  ASTRONOMY. 

those  of  the  majority  of  the  human  race.  We  need 
not  wonder,  therefore,  that  such  homage  is  now  paid 
to  the  genius  of  Newton, — an  admiration  which  has 
been  continually  increasing,  as  new  discoveries  have 
been  made  by  tracing  out  new  consequences  of  the 
law  of  universal  gravitation. 

The  chief  object  of  astronomical  tables  is  to  give 
the  amount  of  all  the  irregularities  that  attend  the  mo- 
tions of  the  heavenly  bodies,  by  estimating  the  separate 
value  of  each,  under  all  the  different  circumstances  in 
which  a  body  can  be  placed.  Thus,  with  respect  to 
the  moon,  before  we  can  determine  accurately  the  dis- 
tance of  the  moon  from  the  vernal  equinox,  that  is,  her 
longitude  at  any  given  moment,  we  must  be  able  to 
make  exact  allowances  for  all  her  irregularities  which 
would  affect  her  longitude.  These  are  in  all  no  less 
than  sixty,  though  most  of  them  are  so  exceedingly 
minute,  that  it  is  not  common  to  take  into  the  account 
more  than  twenty-eight  or  thirty.  The  values  of  these 
are  all  given  in  the  lunar  tables ;  and  in  finding  the 
moon's  place,  at  any  given  time,  we  proceed  as  follows  : 
We  first  find  what  her  place  would  be  on  the  suppo- 
sition that  she  moves  uniformly  in  a  circle.  This  gives 
her  mean  place.  We  next  apply  the  various  correc- 
tions for  her  irregular  motions  ;  that  is,  we  apply  the 
equations,  subtracting  some  and  adding  others,  and 
thus  we  find  her  true  place. 

The  astronomical  tables  have  been  carried  to  such  an 
astonishing  degree  of  accuracy,  that  it  is  said,  by  the 
highest  authority,  that  an  astronomer  could  now  pre- 
dict, for  a  thousand  years  to  come,  the  precise  moment 
of  the  passage  of  any  one  of  the  stars  over  the  merid- 
ian wire  of  the  telescope  of  his  transit-instrument,  with 
such  a  degree  of  accuracy,  that  the  error  would  not  be 
so  great  as  to  remove  the  object  through  an  angular 
space  corresponding  to  the  semidiameter  of  the  finest 
wire  that  could  be  made ;  and  a  body  which,  by  the 
tables,  ought  to  appear  in  the  transit-instrument  in  the 
middle  of  that  wire,  would  in  no  case  be  removed  to 


191 

its  outer  edge.  The  astronomer,  the  mathematician, 
and  the  artist,  have  united  their  powers  to  produce  this 
great  result.  The  astronomer  has  collected  the  data, 
by  long-continued  and  most  accurate  observations  on 
the  actual  motions  of  the  heavenly  bodies,  from  night 
to  night,  and  from  year  to  year  ;  the  mathematician  has 
taken  these  data,  and  applied  to  them  the  boundless 
resources  of  geometry  and  the  calculus ;  and,  finally, 
the  instrument-maker  has  furnished  the  means,  not 
only  of  verifying  these  conclusions,  but  of  discovering 
new  truths,  as  the  foundation  of  future  reasonings. 

Since  the  points  where  the  moon  crosses  the  ecliptic, 
or  the  moon's  nodes,  constantly  shift  their  positions 
about  nineteen  and  a  half  degrees  to  the  westward, 
every  year,  the  sun,  in  his  annual  progress  in  the  eclip- 
tic, will  go  from  the  node  round  to  the  same  node  again 
in  less  time  than  a  year,  since  the  node  goes  to  meet 
him  nineteen  and  a  half  degrees  to  the  west  of  the 
point  where  they  met  before.  It  would  have  taken 
the  sun  about  nineteen  days  to  have  passed  over  this 
arc ;  and  consequently,  the  interval  between  two  suc- 
cessive conjunctions  between  the  sun  and  the  moon's 
node  is  about  nineteen  days  shorter  than  the  solar  year 
of  three  hundred  and  sixty-five  days ;  that  is,  it  is 
about  three  hundred  and  forty-six  days ;  or,  more  ex- 
actly, it  is  346.619851  days.  The  time  from  one  new 
moon  to  another  is  29.5305887  days.  Now,  nineteen 
of  the  former  periods  are  almost  exactly  equal  to  two 
hundred  and  twenty-three  of  the  latter : 

For    346.619851  X    19=6585.78  days=18  y.  10  d. 

And  29.5305887X223=6585.32      "  =  «   "    "  " 

Hence,  if  the  sun  and  moon  were  to  leave  the 
moon's  node  together,  after  the  sun  had  been  round  to 
the  same  node  nineteen  times,  the  moon  would  have 
made  very  nearly  two  hundred  and  twenty-three  con- 
junctions with  the  sun.  If,  therefore,  she  was  in  con- 
junction with  the  sun  at  the  beginning  of  this  period, 
she  would  be  in  conjunction  again  at  the  end  of  it; 
and  all  things  relating  to  the  sun,  the  moon,  and  the 


192  LETTERS   ON  ASTRONOMY. 

node,  would  be  restored  to  the  same  relative  situation 
as  before,  and  the  sun  and  moon  would  start  again,  to 
repeat  the  same  phenomena,  arising  out  of  these  rela- 
tions, as  occurred  in  the  preceding  period,  and  in  the 
same  order.  Now,  when  the  sun  and  moon  meet  at 
the  moon's  node,  an  eclipse  of  the  sun  happens  ;  and 
during  the  entire  period  of  eighteen  and  a  half  years 
eclipses  will  happen,  nearly  in  the  same  manner  as  they 
did  at  corresponding  times  in  the  preceding  period. 
Thus,  if  there  was  a  great  eclipse  of  the  sun  on  the 
fifth  year  of  one  of  these  periods,  a  similar  eclipse 
(usually  differing  somewhat  in  magnitude)  might  be 
expected  on  the  fifth  year  of  the  next  period.  Hence 
this  period,  consisting  of  about  eighteen  years  and  ten 
days,  under  the  name  of  the  Saros,  was  used  by  the 
Chaldeans,  and  other  ancient  nations,  in  predicting 
eclipses.  It  was  probably  by  this  means  that  Thales,  a 
Grecian  astronomer  who  flourished  six  hundred  years 
before  the  Christian  era,  predicted  an  eclipse  of  the  sun. 
Herodotus,  the  old  historian  of  Greece,  relates  that  the 
day  was  suddenly  changed  into  night,  and  that  Thales 
of  Miletus  had  foretold  that  a  great  eclipse  was  to  hap- 
pen this  year.  It  was  therefore,  at  that  age,  considered 
as  a  distinguished  feat  to  predict  even  the  year  in  which 
an  eclipse  was  to  happen.  This  eclipse  is  memorable 
in  ancient  history,  from  its  having  terminated  the  war 
between  the  Lydians  and  the  Medes,  both  parties  being 
smitten  with  such  indications  of  the  wrath  of  the  gods. 
The  Metonic  Cycle  has  sometimes  been  confounded 
with  the  Saros,  but  it  is  not  the  same  with  it,  nor  was 
the  period  used,  like  the  Saros,  for  foretelling  eclipses, 
but  for  ascertaining  the  age  of  the  moon  at  any  given 
period.  It  consisted  of  nineteen  tropical  years,  during 
which  time  there  are  exactly  two  hundred  and  thirty- 
five  new  moons  ;  so  that,  at  the  end  of  this  period,  the 
new  moons  will  recur  at  seasons  of  the  year  correspon- 
ding exactly  to  those  of  the  preceding  cycle.  If,  for 
example,  a  new  moon  fell  at  the  time  of  the  vernal  equi- 
nox, in  one  cycle,  nineteen  years  afterwards  it  would 


193 

occur  again  at  the  same  equinox ;  or,  if  it  had  happen- 
ed ten  days  after  the  equinox,  in  one  cycle,  it  would 
also  happen  ten  days  after  the  equinox,  nineteen  years 
afterwards.  By  registering,  therefore,  the  exact  days 
of  any  cycle  at  which  the  new  or  full  moons  occurred, 
such  a  calendar  would  show  on  what  days  these  events 
would  occur  in  any  other  cycle  ;  and,  since  the  regula- 
tion of  games,  feasts,  and  fasts,  has  been  made  very  ex- 
tensively, both  in  ancient  and  modern  times,  according 
to  new  or  full  moons,  such  a  calendar  becomes  very  con- 
venient for  finding  the  day  on  which  the  new  or  full 
moon  required  takes  place.  Suppose,  for  example,  it 
were  decreed  that  a  festival  should  be  held  on  the  day 
of  the  first  full  moon  after  the  Vernal  equinox.  Then, 
to  find  on  what  day  that  would  happen,  in  any  given 
year,  we  have  only  to  see  what  year  it  is  of  the  lunar 
cycle ;  for  the  day  will  be  the  same  as  it  was  in  the 
corresponding  year  of  the  calendar  which  records  all 
the  full  moons  of  the  cycle  for  each  year,  and  the  re- 
spective days  on  which  they  happen. 

The  Athenians  adopted  the  metonic  cycle  four  hun- 
dred and  thirty-three  years  before  the  Christian  era, 
for  the  regulation  of  their  calendars,  and  had  it  inscribed 
in  letters  of  gold  on  the  walls  of  the  temple  of  Minerva. 
Hence  the  term  golden  number,  still  found  in  our  al- 
manacs, which  denotes  the  year  of  the  lunar  cycle, 
Thus,  fourteen  was  the  golden  number  for  1837,  being 
the  fourteenth  year  of  the  lunar  cycle. 

The  inequalities  of  the  moon's  motions  are  divided 
into  periodical  and  secular.  Periodical  inequalities 
are  those  which  are  completed  in  comparatively  short 
periods.  Secular  inequalities  are  those  which  are  com- 
pleted only  in  very  long  periods,  such  as  centuries  or 
ages.  Hence  the  corresponding  terms  periodical  equa- 
tions and  secular  equations.  As  an  example  of  a  sec- 
ular inequality,  we  may  mention  the  acceleration  of  the 
moon's  mean  motion.  It  is  discovered  that  the  moon 
actually  revolves  around  the  earth  in  a  less  period  now 
than  she  did  in  ancient  times.  The  difference,  howev- 
17  L.  A. 


194  LETTERS  ON  ASTRONOMY. 

er,  is  exceedingly  small,  being  only  about  ten  seconds  in 
a  century.  In  a  lunar  eclipse,  the  moon's  longitude  dif- 
fers from  that  of  the  sun,  at  the  middle  of  the  eclipse, 
by  exactly  one  hundred  and  eighty  degrees ;  and 
since  the  sun's  longitude  at  any  given  time  of  the  year 
is  known,  if  we  can  learn  the  day  and  hour  when  an 
eclipse  occurred  at  any  period  of  the  world,  we  of  course 
know  the  longitude  of  the  sun  and  moon  at  that  pe- 
riod. Now,  in  the  year  721,  before  the  Christian  era, 
Ptolemy  records  a  lunar  eclipse  to  have  happened,  and 
to  have  been  observed  by  the  Chaldeans.  The  moon's 
longitude,  therefore,  for  that  time,  is  known  ;  and  as 
we  know  the  mean  motions  of  the  moon,  at  present, 
starting  from  that  epoch,  and  computing,  as  may  easi- 
ly be  done,  the  place  which  the  moon  ought  to  occupy 
at  present,  at  any  given  time,  she  is  found  to  be  actual- 
ly nearly  a  degree  and  a  half  in  advance  of  that  place. 
Moreover,  the  same  conclusion  is  derived  from  a  com- 
parison of  the  Chaldean  observations  with  those  made 
by  an  Arabian  astronomer  of  the  tenth  century. 

This  phenomenon  at  first  led  astronomers  to  appre- 
hend that  the  moon  encountered  a  resisting  medium, 
which,  by  destroying  at  every  revolution  a  small  portion 
of  her  projectile  force,  would  have  the  effect  to  bring 
her  nearer  and  nearer  to  the  earth,  and  thus  to  aug- 
ment her  velocity.  But,  in  1786,  La  Place  demonstra- 
ted that  this  acceleration  is  one  of  the  legitimate  ef- 
fects of  the  sun's  disturbing  force,  and  is  so  connected 
with  changes  in  the  eccentricity  of  the  earth's  orbit, 
that  the  moon  will  continue  to  be  accelerated  while  that 
eccentricity  diminishes ;  but  when  the  eccentricity  has 
reached  its  minimum,  or  lowest  point,  (as  it  will  do, 
after  many  ages,)  and  begins  to  increase,  then  the 
moon's  motions  will  begin  to  be  retarded,  and  thus  her 
mean  motions  will  oscillate  for  ever  about  a  mean  value. 


ECLIPSES.  195 


LETTER  XVIII. 

ECLIPSES. 

"  As  when  the  sun,  new  risen, 

Looks  through  the  horizontal  misty  air, 
Shorn  of  his  beams,  or  from  behind  the  moon, 
In  dim  eclipse,  disastrous  twilight  sheds 
On  half  the  nations,  and  with  fear  of  change 
Perplexes  monarchs  :  darkened  so,  yet  shone, 
Above  them  all,  the  Archangel."— Milton. 

HAVING  now  learned  various  particulars  respecting 
the  earth,  the  sun,  and  the  moon,  you  are  prepared  to 
understand  the  explanation  of  solar  and  lunar  eclipses, 
which  have  in  all  ages  excited  a  high  degree  of  interest. 
Indeed,  what  is  more  admirable,  than  that  astronomers 
should  be  able  to  tell  us,  years  beforehand,  the  exact 
instant  of  the  commencement  and  termination  of  an 
eclipse,  and  describe  all  the  attendant  circumstances 
with  the  greatest  fidelity.  You  have  doubtless,  my 
dear  friend,  participated  in  this  admiration,  and  felt  a 
strong  desire  to  learn  how  it  is  that  astronomers  are  able 
to  look  so  far  into  futurity.  I  will  endeavor,  in  this  Let- 
ter, to  explain  to  you  the  leading  principles  of  the  cal- 
culation of  eclipses,  with  as  much  plainness  as  possible. 

An  eclipse  of  the  moon  happens  when  the  moon,  in 
its  revolution  around  the  earth,  falls  into  the  earth's 
shadow.  An  eclipse  of  the  sun  happens  when  the 
moon,  coming  between  the  earth  and  the  sun,  covers 
either  a  part  or  the  whole  of  the  solar  disk. 

The  earth  and  the  moon  being  both  opaque,  globular 
bodies,  exposed  to  the  sun's  light,  they  cast  shadows 
opposite  to  the  sun,  like  any  other  bodies  on  which  the 
sun  shines.  Were  the  sun  of  the  same  size  with  the 
earth  and  the  moon,  then  the  lines  drawn  touching  the 
surface  of  the  sun  and  the  surface  of  the  earth  or  moon 
(which  lines  form  the  boundaries  of  the  shadow)  would 
be  parallel  to  each  other,  and  the  shadow  would  be  a 
cylinder  infinite  in  length ;  and  were  the  sun  less  than 


196 


LETTERS   ON  ASTKONOMY. 


the  earth  or  the  moon,  the  shadow  would  be  an  increas- 
ing cone,  its  narrower  end  resting  on  the  earth  ;  but  as 
the  sun  is  vastly  greater  than  either  of  these  bodies, 
the  shadow  of  each  is  a  cone  whose  base  rests  on  the 
body  itself,  and  which  comes  to  a  point,  or  vertex,  at  a 
certain  distance  behind  the  body.  These  several  cases 
are  represented  in  the  following  diagrams,  Figs.  39, 
40,  41. 

Figs.  39,  40,  41. 


It  is  found,  by  calculation,  that  the  length  of  the 
moon's  shadow,  on  an  average,  is  just  about  sufficient 
to  reach  to  the  earth  ;  but  the  moon  is  sometimes  fur- 
ther fjom  the  earth  than  at  others,  and  when  she  is 
nearer  than  usual,  the  shadow  reaches  considerably  be- 
yond the  surface  of  the  earth.  Also,  the  moon,  as  well 
as  the  earth,  is  at  different  distances  from  the  sun  at 
different  times,  and  its  shadow  is  longest  when  it  is 
furthest  from  the  sun.  Now,  when  both  these  circum- 
stances conspire,  that  is,  when  the  moon  is  in  her  peri- 
gee and  along  with  the  earth  in  her  aphelion,  her  shad- 
ow extends  nearly  fifteen  thousand  miles  beyond  the 
centre  of  the  earth,  and  covers  a  space  on  the  surface 
one  hundred  and  seventy  miles  broad.  The  earth's 
shadow  is  nearly  a  million  of  miles  in  length,  and  con- 
sequently more  than  three  and  a  half  times  as  long  as 
the  distance  of  the  earth  from  the  moon  ;  and  it  is  also, 
at  the  distance  of  the  moon,  three  times  as  broad  as  the 
moon  itself. 


ECLIPSES.  197 

An  eclipse  of  the  sun  can  take  place  only  at  new 
moon,  when  the  sun  and  moon  meet  in  the  same  part 
of  the  heavens,  for  then  only  can  the  moon  come  be- 
tween us  and  the  sun  ;  and  an  eclipse  of  the  moon  can 
occur  only  when  the  sun  and  moon  are  in  opposite  parts 
of  the  heavens,  or  at  full  moon  ;  for  then  only  can  the 
moon  fall  into  the  shadow  of  the  earth. 

The  nature  of  eclipses  will  be  clearly  understood  from 
the  following  representation.  The  diagram,  Fig.  42,  ex- 
Fig.  42. 


hibits  the  relative  position  of  the  sun,  the  earth,  and  the 
moon,  both  in  a  solar  and  in  a  lunar  eclipse.  Here,  the 
moon  is  first  represented,  while  revolving  round  the 
earth,  as  passing  between  the  earth  and  the  sun,  and 
casting  its  shadow  on  the  earth.  As  the  moon  is  here 
supposed  to  be  at  her  average  distance  from  the  earth, 
the  shadow  but  just  reaches  the  earth's  surface.  Were 
the  moon  (as  is  sometimes  the  case)  nearer  the  earth, 
her  shadow  would  not  terminate  in  a  point,  as  is  repre- 
sented in  the  figure,  but  at  a  greater  or  less  distance 
nearer  the  base  of  the  cone,  so  as  to  cover  a  considera- 
ble space,  which,  as  I  have  already  mentioned,  some- 
times extends  to  one  hundred  and  seventy  miles  in 
breadth,  but  is  commonly  much  less  than  this.  On  the 
other  side  of  the  earth,  the  moon  is  represented  as 
traversing  the  earth's  shadow,  as  is  the  case  in  a  lunar 
17* 


198  LETTERS  ON  ASTRONOMY. 

eclipse.  As  the  moon  is  sometimes  nearer  the  earth 
and  sometimes  further  off,  it  is  evident  that  it  will  trav- 
erse the  shadow  at  a  broader  or  a  narrower  part,  ac- 
cordingly. The  figure,  however,  represents  the  moon 
as  passing  the  shadow  further  from  the  earth  than  is 
ever  actually  the  case,  since  the  distance  from  the  earth 
is  never  so  much  as  one  third  of  the  whole  length  of  the 
shadow. 

It  is  evident  from  the  figure,  that  if  a  spectator  were 
situated  where  the  moon's  shadow  strikes  the  earth,  the 
moon  would  cut  off  from  him  the  view  of  the  sun,  or 
the  sun  would  be  totally  eclipsed.  Or,  if  he  were 
within  a  certain  distance  of  the  shadow  on  either  side, 
the  moon  would  be  partly  between  him  and  the  sun, 
and  would  intercept  from  him  more  or  less  of  the  sun's 
light,  according  as  he  was  nearer  to  the  shadow  or  fur- 
ther from  it.  If  he  were  at  c  or  d,  he  would  just  see 
the  moon  entering  upon  the  sun's  disk ;  if  he  were 
nearer  the  shadow  than  either  of  these  points,  he  would 
have  a  portion  of  this  light  cut  off  from  his  view,  and 
more,  in  proportion  as  he  drew  nearer  the  shadow ; 
and  the  moment  he  entered  the  shadow,  he  would  lose 
sight  of  the  sun.  To  all  places  between  a  or  b  and  the 
shadow,  the  sun  would  cast  a  partial  shadow  of  the 
moon,  growing  deeper  and  deeper,  as  it  approached  the 
true  shadow.  This  partial  shadow  is  called  the  moon's 
penumbra.  In  like  manner,  as  the  moon  approaches 
the  earth's  shadow,  in  a  lunar  eclipse,  as  soon  as  she 
arrives  at  a,  the  earth  begins  to  intercept  from  her  a 
portion  of  the  sun's  light,  or  she  falls  in  the  earth's 
penumbra.  She  continues  to  lose  more  and  more  of 
the  sun's  light,  as  she  draws  near  to  the  shadow,  and 
hence  her  disk  becomes  gradually  obscured,  until  it  en- 
ters the  shadow,  when  the  sun's  light  is  entirely  lost. 

As  the  sun  and  earth  are  both  situated  in  the  plane 
of  the  ecliptic,  if  the  moon  also  revolved  around  the 
earth  in  this  plane,  we  should  have  a  solar  eclipse  at 
every  new  moon,  and  a  lunar  eclipse  at  every  full 
moon ;  for,  in  the  former  case,  the  moon  would  come 


ECLIPSES.  199 

directly  between  us  and  the  sun,  and  in  the  latter  case, 
the  earth  would  come  directly  between  the  sun  and 
the  moon.  But  the  moon  is  inclined  to  the  ecliptic 
about  five  degrees,  and  the  centre  of  the  moon  may  be 
all  this  distance  from  the  centre  of  the  sun  at  new  moon, 
and  the  same  distance  from  the  centre  of  the  earth's 
shadow  at  full  moon.  It  is  true,  the  moon  extends 
across  her  path,  one  half  her  breadth  lying  on  each  side 
of  it,  and  the  sun  likewise  reaches  from  the  ecliptic  a 
distance  equal  to  half  his  breadth.  But  these  luminaries 
together  make  but  little  more  than  a  degree,  and  con- 
sequently, their  two  semidiameters  would  occupy  only 
about  half  a  degree  of  the  five  degrees  from  one  orbit  to 
to  the  other  where  they  are  furthest  apart.  Also,  the 
earth's  shadow,  where  the  moon  crosses  it,  extends  from 
the  ecliptic  less  than  three  fourths  of  a  degree,  so  that 
the  semidiameter  of  the  moon  and  of  the  earth's  shad- 
ow would  together  reach  but  little  way  across  the  space 
that  may,  in  certain  cases,  separate  the  two  luminaries 
from  each  other  when  they  are  in  opposition.  Thus, 
suppose  we  could  take  hold  of  the  circle  in  the  figure  that 
represents  the  moon's  orbit,  (Fig.  42,  page  197,)  and  lift 
the  moon  up  five  degrees  above  the  plane  of  the  paper,  it 
is  evident  that  the  moon,  as  seen  from  the  earth,  would 
appear  in  the  heavens  five  degrees  above  the  sun,  and 
of  course  would  cut  off  none  of  his  light ;  and  it  is  also 
plain  that  the  moon,  at  the  full,  would  pass  the  shadow 
of  the  earth  five  degrees  below  it,  and  would  suffer  no 
eclipse.  But  in  the  course  of  the  sun's  apparent  revo- 
lution round  the  earth  once  a  year  he  is  successively  in 
every  part  of  the  ecliptic ;  consequently,  the  conjunc- 
tions and  oppositions  of  the  sun  and  moon  may  occur 
at  any  part  of  the  ecliptic,  and  of  course  at  the  two 
points  where  the  moon's  orbit  crosses  the  ecliptic, — 
that  is,  at  the  nodes  ;  for  the  sun  must  necessarily  come 
to  each  of  these  nodes  once  a  year.  If,  then,  the  moon 
overtakes  the  sun  just  as  she  is  crossing  his  path,  she 
will  hide  more  or  less  of  his  disk  from  us.  Since,  also, 
the  earth's  shadow  is  always  directly  opposite  to  the 


200  LETTERS  ON  ASTRONOMY. 

sun,  if  the  sun  is  at  one  of  the  nodes,  the  shadow  must 
extend  in  the  direction  of  the  other  node,  so  as  to  lie 
directly  across  the  moon's  path  ;  and  if  the  moon  over- 
takes it  there,  she  will  pass  through  it,  and  be  eclipsed. 
Thus,  in  Fig.  43,  let  B  N  represent  the  sun's  path,  and 

Fig.  43. 


A  N,  the  moon's, — N  being  the  place  of  the  node ; 
then  it  is  evident,  that  if  the  two  luminaries  at  new 
moon  be  so  far  from  the  node,  that  the  distances  be- 
tween their  centres  is  greater  than  their  semidiameters, 
no  eclipse  can  happen  ;  but  if  that  distance  is  less  than 
this  sum,  as  at  E,  F,  then  an  eclipse  will  take  place  ; 
but  if  the  position  be  as  at  C,  D,  the  two  bodies  vv7ill 
just  touch  one  another.  If  A  denotes  the  earth's  shad- 
ow, instead  of  the  sun,  the  same  illustration  will  apply 
to  an  eclipse  of  the  moon. 

Since  bodies  are  defined  to  be  in  conjunction  when 
they  are  in  the  same  part  of  the  heavens,  and  to  be  in 
opposition  when  they  are  in  opposite  parts  of  the  heav- 
ens, it  may  not  appear  how  the  sun  and  moon  can  be  in 
conjunction,  as  at  A  and  B,  when  they  are  still  at  some 
distance  from  each  other.  But  it  must  be  recollected 
that  bodies  are  in  conjunction  when  they  have  the  same 
longitude,  in  which  case  they  are  situated  in  the  same 
great  circle  perpendicular  to  the  ecliptic, — that  is,  in 
the  same  secondary  to  the  ecliptic.  One  of  these  bod- 
ies may  be  much  further  from  the  ecliptic  than  the  oth- 
er ;  still,  if  the  same  secondary  to  the  ecliptic  passes 


ECLIPSES.  201 

through  them  both,  they  will  be  in  conjunction  or  op- 
position. 

In  a  total  eclipse  of  the  moon,  its  disk  is  still  visible, 
shining  with  a  dull,  red  light.  This  light  cannot  be 
derived  directly  from  the  sun,  since  the  view  of  the  sun 
is  completely  hidden  from  the  moon  ;  nor  by  reflection 
from  the  earth,  since  the  illuminated  side  of  the  earth  is 
wholly  turned  from  the  moon  ;  but  it  is  owing  to  refrac- 
tion from  the  earth's  atmosphere,  by  which  a  few  scat- 
tered rays  of  the  sun  are  bent  round  into  the  earth's 
shadow  and  conveyed  to  the  moon,  sufficient  in  number 
to  afford  the  feeble  light  in  question. 

It  is  impossible  fully  to  understand  the  method  of 
calculating  eclipses,  without  a  knowledge  of  trigonom- 
etry ;  still  it  is  not  difficult  to  form  some  general  notion 
of  the  process.  It  may  be  readily  conceived  that,  by 
long-continued  observations  on  the  sun  and  moon,  the 
laws  of  their  revolution  may  be  so  well  understood,  that 
the  exact  places  which  they  will  occupy  in  the  heavens 
at  any  future  times  may  be  foreseen  and  laid  down  in 
tables  of  the  sun  and  moon's  motions;  that  we  may 
thus  ascertain,  by  inspecting  the  tables,  the  instant  when 
these  two  bodies  will  be  together  in  the  heavens,  or  be 
in  conjunction,  and  when  they  will  be  one  hundred  and 
eighty  degrees  apart,  or  in  opposition.  Moreover,  since 
the  exact  place  of  the  moon's  node  among  the  stars  at 
any  particular  time  is  known  to  astronomers,  it  cannot 
be  difficult  to  determine  when  the  new  or  full  moon 
occurs  in  the  same  part  of  the  heavens  as  that  where 
the  node  is  projected,  as  seen  from  the  earth.  In  short, 
as  astronomers  can  easily  determine  what  will  be  the 
relative  position  of  the  sun,  the  moon,  and  the  moon's 
nodes,  for  any  given  time,  they  can  tell  when  these 
luminaries  will  meet  so  near  the  node  as  to  produce 
an  eclipse  of  the  sun,  or  when  they  will  be  in  opposi- 
tion so  near  the  node  as  to  produce  an  eclipse  of  the 
moon. 

A  little  reflection  will  enable  you  to  form  a  clear  idea 
of  the  situation  of  the  sun,  the  moon,  and  the  earth,  at 


202  LETTERS  ON  ASTRONOMY. 

the  time  of  a  solar  eclipse.  First,  suppose  the  con- 
junction to  take  place  at  the  node  ;  that  is,  imagine  the 
moon  to  come  directly  between  the  earth  and  the  sun, 
as  she  will  of  course  do,  if  she  comes  between  the  earth 
and  the  sun  the  moment  she  is  crossing  the  ecliptic ;  for 
then  the  three  bodies  will  all  lie  in  one  and  the  same 
straight  line.  But  when  the  moon  is  in  the  ecliptic, 
her  shadow,  or  at  least  the  axis,  or  central  line,  of  the 
shadow,  must  coincide  with  the  line  that  joins  the  cen- 
tres of  the  sun  and  earth,  arid  reach  along  the  plane  of 
the  ecliptic  towards  the  earth.  The  moon's  shadow, 
at  her  average  distance  from  the  earth,  is  just  about 
long  enough  to  reach  the  surface  of  the  earth ;  but 
when  the  moon,  at  the  new,  is  in  her  apogee,  or  at  her 
greatest  distance  from  the  earth,  the  shadow  is  not  long 
enough  to  reach  the  earth.  On  the  contrary,  when  the 
moon  is  nearer  to  us  than  her  average  distance,  her 
shadow  is  long  enough  to  reach  beyond  the  earth,  ex- 
tending, when  the  moon  is  in  her  perigee,  more  than 
fourteen  thousand  miles  beyond  the  centre  of  the  earth. 
Now,  as  during  the  eclipse  the  moon  moves  nearly  in 
the  plane  of  the  ecliptic,  her  shadow  which  accompa- 
nies her  must  also  move  nearly  in  the  same  plane,  and 
must  therefore  traverse  the  earth  across  its  central  re- 
gions, along  the  terrestrial  ecliptic,  since  this  is  nothing 
more  than  the  intersection  of  the  plane  of  the  celestial 
ecliptic  with  the  earth's  surface.  The  motion  of  the 
earth,  too,  on  its  axis,  in  the  same  direction,  will  carry 
a  place  along  with  the  shadow,  though  with  a  less  ve- 
locity by  more  than  one  half ;  so  that  the  actual  veloc- 
ity of  the  shadow,  in  respect  to  places  over  which  it 
passes  on  the  earth,  will  only  equal  the  difference  be- 
tween its  own  rate  and  that  of  the  places,  as  they  are 
carried  forward  in  the  diurnal  revolution. 

We  have  thus  far  supposed  that  the  moon  comes  to 
her  conjunction  precisely  at  the  node,  or  at  the  moment 
when  she  is  crossing  the  ecliptic.  But,  secondly,  sup- 
pose she  is  on  the  north  side  of  the  ecliptic  at  the  time 
of  conjunction,  and  moving  towards  her  descending 


ECLIPSES.  203 

node,  and  that  the  conjunction  takes  place  as  far  from 
the  node  as  an  eclipse  can  happen.  The  shadow  will 
not  fall  in  the  plane  of  the  ecliptic,  but  a  little  north- 
ward of  it,  so  as  just  to  graze  the  earth  near  the  pole 
of  the  ecliptic.  The  nearer  the  conjunction  comes  to 
the  node,  the  further  the  shadow  will  fall  from  the  polar 
towards  the  equatorial  regions. 

In  a  solar  eclipse,  the  shadow  of  the  moon  travels 
over  a  portion  of  the  earth,  as  the  shadow  of  a  small 
cloud,  seen  from  an  eminence  in  a  clear  day,  rides  along 
over  hills  and  plains.  Let  us  imagine  ourselves  stand- 
ing on  the  moon ;  then  we  shall  see  the  earth  partially 
eclipsed  by  the  moon's  shadow,  in  the  same  manner  as 
we  now  see  the  moon  eclipsed  by  the  shadow  of  the 
earth ;  and  we  might  calculate  the  various  circumstan- 
ces of  the  eclipse, — its  commencement,  duration,  and 
quantity, — in  the  same  manner  as  we  calculate  these 
elements  in  an  eclipse  of  the  moon,  as  seen  from  the 
earth.  But  although  the  general  characters  of  a  solar 
eclipse  might  be  investigated  on  these  principles,  so  far 
as  respects  the  earth  at  large,  yet,  as  the  appearances  of 
the  same  eclipse  of  the  sun  are  very  different  at  differ- 
ent places  on  the  earth's  surface,  it  is  necessary  to  calcu- 
late its  peculiar  aspects  for  each  place  separately,  a  cir- 
cumstance which  makes  the  calculation  of  a  solar  eclipse 
much  more  complicated  and  tedious  than  that  of  an 
eclipse  of  the  moon.  The  moon,  when  she  enters  the 
shadow  of  the  earth,  is  deprived  of  the  light  of  the  part 
immersed,  and  the  effect  upon  its  appearance  is  the 
same  as  though  that  part  were  painted  black,  in  which 
case  it  would  be  black  alike  to  all  places  where  the 
moon  was  above  the  horizon.  But  it  not  so  with  a  so- 
lar eclipse.  We  do  not  see  this  by  the  shadow  cast  on 
the  earth,  as  we  should  do,  if  we  stood  on  the  moon, 
but  by  the  interposition  of  the  moon  between  us  and 
the  sun  ;  and  the  sun  may  be  hidden  from  one  observ- 
er, while  he  is  in  full  view  of  another  only  a  few  miles 
distant.  Thus,  a  small  insulated  cloud  sailing  in  a  clear 
sky  will,  for  a  few  moments,  hide  the  sun  from  us, 


204  LETTERS  ON  ASTRONOMY. 

and  from  a  certain  space  near  us,  while  all  the  region 
around  is  illuminated.  But  although  the  analogy  be- 
tween the  motions  of  the  shadow  of  a  small  cloud  and 
of  the  moon  in  a  solar  eclipse  holds  good  in  many  par- 
ticulars, yet  the  velocity  of  the  lunar  shadow  is  far 
greater  than  that  of  the  cloud,  being  no  less  than  two 
thousand  two  hundred  and  eighty  miles  per  hour. 

The  moon's  shadow  can  never  cover  a  space  on  the 
earth  more  than  one  hundred  and  seventy  miles  broad, 
and  the  space  actually  covered  commonly  falls  much 
short  of  that.  The  portion  of  the  earth's  surface  ever 
covered  by  the  moon's  penumbra  is  about  four  thous- 
and three  hundred  and  ninety-three  miles. 

The  apparent  diameter  of  the  moon  varies  material- 
ly at  different  times,  being  greatest  when  the  moon  is 
nearest  to  us,  and  least  when  she  is  farthest  off;  while 
the  sun's  apparent  dimensions  remain  nearly  the  same. 
When  the  moon  is  at  her  average  distance  from  the 
earth,  she  is  just  about  large  enough  to  cover  the  sun's 
disk ;  consequently,  if,  in  a  central  eclipse  of  the  sun, 
the  moon  is  at  her  mean  distance,  she  covers  the  sun 
but  for  an  instant,  producing  only  a  momentary  eclipse. 
If  she  is  nearer  than  her  average  distance,  then  the 
eclipse  may  continue  total  some  time,  though  never  more 
than  eight  minutes,  and  seldom  so  long  as  that ;  but  if 
she  is  further  off  than  usual,  or  towards  her  apogee,  then 
she  is  not  large  enough  to  cover  the  whole  solar  disk, 
but  we  see  a  ring  of  the  sun  encircling  the  moon,  con- 
stituting an  annular  eclipse,  as  seen  in  Fig.  44.  Even 
the  elevation  of  the  moon  above  the  horizon  will  some- 
times sensibly  affect  the  dimensions  of  the  eclipse.  You 
will  recollect  that  the  moon  is  nearer  to  us  when  on 
the  meridian  than  when  in  the  horizon  by  nearly  four 
thousand  miles,  or  by  nearly  the  radius  of  the  earth  ; 
and  consequently,  her  apparent  diameter  is  largest  when 
on  the  meridian.  The  difference  is  so  considerable, 
that  the  same  eclipse  will  appear  total  to  a  spectator 
who  views  it  near  his  meridian,  while,  at  the  same 
moment,  it  appears  annular  to  one  who  has  the  moon 


205 


near  his  horizon.     An  annular  eclipse  may  last,  at  most, 
twelve  minutes  and  twenty-four  seconds. 

Eclipses  of  the  sun  are  more  frequent  than  those  of 
the  moon.  Yet  lunar  eclipses  being  visible  to  every 
part  of  the  terrestrial  hemisphere  opposite  to  the  sun, 
while  those  of  the  sun  are  visible  only  to  a  small  por- 
tion of  the  hemisphere  on  which  the  moon's  shadow 
falls,  it  happens  that,  for  any  particular  place  on  the 
earth,  lunar  eclipses  are  more  frequently  visible  than 
solar.  In  any  year,  the  number  of  eclipses  of  both 
luminaries  cannot  be  less  than  two  nor  more  than  sev- 
en :  the  most  usual  number  is  four,  and  it  is  very  rare 
to  have  more  than  six.  A  total  eclipse  of  the  moon  fre- 
quently happens  at  the  next  full  moon  after  an  eclipse 
of  the  sun.  For  since,  in  a  solar  eclipse,  the  sun  is  at 
or  near  one  of  the  moon's  nodes, — that  is,  is  projected 
to  the  place  in  the  sky  where  the  moon  crosses  the 
ecliptic, — the  earth's  shadow,  which  is  of  course  di- 
rectly opposite  to  the  sun,  must  be  at  or  near  the  other 
node,  and  may  not  have  passed  too  far  from  the  node 
before  the  moon  comes  round  to  the  opposition  and 

18  L.  A. 


206  LETTERS  ON  ASTRONOMY. 

overtakes  it.  In  total  eclipses  of  the  sun,  there  has 
sometimes  been  observed  a  remarkable  radiation  of  light 
from  the  margin  of  the  sun,  which  is  thought  to  be  owing 
to  the  zodiacal  light,  which  is  of  such  dimensions  as  to 
extend  far  beyond  the  solar  orb.  A  striking  appear- 
ance of  this  kind  was  exhibited  in  the  total  eclipse  of 
the  sun  which  occurred  in  June,  1806. 

A  total  eclipse  of  the  sun  is  one  of  the  most  sublime 
and  impressive  phenomena  of  Nature.  Among  barba- 
rous tribes  it  is  ever  contemplated  with  fear  and  aston- 
ishment, and  as  strongly  indicative  of  the  displeasure 
of  the  gods.  Two  ancient  nations,  the  Lydians  and 
Medes,  alluded  to  before,  who  were  engaged  in  a  bloody 
war,  about  six  hundred  years  before  Christ,  were  smit- 
ten with  such  awe,  on  the  appearance  of  a  total  eclipse 
of  the  sun,  just  on  the  eve  of  a  battle,  that  they  threw 
down  their  arms,  and  made  peace.  When  Columbus 
first  discovered  America,  and  was  in  danger  of  hostility 
from  the  Natives,  he  awed  them  into  submission  by 
telling  them  that  the  sun  would  be  darkened  on  a  cer- 
tain day,  in  token  of  the  anger  of  the  gods  at  them,  for 
their  treatment  of  him. 

Among  cultivated  nations,  a  total  eclipse  of  the  sun 
is  recognised,  from  the  exactness  with  which  the  time 
of  occurrence  and  the  various  appearances  answer  to 
the  prediction,  as  affording  one  of  the  proudest  tri- 
umphs of  astronomy.  By  astronomers  themselves,  it  is 
of  course  viewed  with  the  highest  interest,  not  only  as 
verifying  their  calculations,  but  as  contributing  to  estab- 
lish, beyond  all  doubt,  the  certainty  of  those  grand  laws, 
the  truth  of  which  is  involved  in  the  result.  I  had  the 
good  fortune  to  witness  the  total  eclipse  of  the  sun  of 
June,  1806,  which  was  one  of  the  most  remarkable  on 
record.  To  the  wondering  gaze  of  childhood  it  present- 
ed a  spectacle  that  can  never  be  forgotten.  A  bright  and 
beautiful  morning  inspired  universal  joy,  for  the  sky  was 
entirely  cloudless.  Every  one  was  busily  occupied  in 
preparing  smoked  glass,  in  readiness  for  the  great  sight, 
which  was  to  be  first  seen  about  ten  o'clock.  A  thrill 


ECLIPSES.  207 

of  mingled  wonder  and  delight  struck  every  mind  when, 
at  the  appointed  moment,  a  little  black  indentation 
appeared  on  the  limb  of  the  sun.  This  gradually  ex- 
panded, covering  more  and  more  of  the  solar  disk,  until 
an  increasing  gloom  was  spread  over  the  face  of  Nature  ; 
and  when  the  sun  was  wholly  lost,  near  mid-day,  a  feel- 
ing of  horror  pervaded  almost  every  beholder.  The 
darkness  was  wholly  unlike  that  of  twilight  or  night. 
A  thick  curtain,  very  different  from  clouds,  hung  upon 
the  face  of  the  sky,  producing  a  strange  and  indescrib- 
ably gloomy  appearance,  which  was  reflected  from  all 
things  on  the  earth,  in  hues  equally  strange  and  unnat- 
ural. Some  of  the  planets,  and  the  largest  of  the  fixed 
stars,  shone  out  through  the  gloom,  yet  with  their  usual 
brightness.  The  temperature  of  the  air  rapidly  de- 
clined, and  so  sudden  a  chill  came  over  the  earth,  that 
many  persons  caught  severe  colds  from  their  exposure. 
Even  the  animal  tribes  exhibited  tokens  of  fear  and 
agitation.  Birds,  especially,  fluttered  and  flew  swiftly 
about,  and  domestic  fowls  went  to  rest. 

Indeed,  the  word  eclipse  is  derived  from  a  Greek  word, 
(exleiyis,  ekleipsis,)  which  signifies  to  fail,  to  faint  or 
swoon  away ;  since  the  moon,  at  the  period  of  her  great- 
est brightness,  falling  into  the  shadow  of  the  earth,  was 
imagined  by  the  ancients  to  sicken  and  swoon,  as  if 
she  were  going  to  die.  By  some  very  ancient  nations 
she  was  supposed,  at  such  times,  to  be  in  pain  ;  and,  in 
order  to  relieve  her  fancied  distress,  they  lifted  torches 
high  in  the  atmosphere,  blew  horns  and  trumpets,  beat 
upon  brazen  vessels,  and  even,  after  the  eclipse  was 
over,  they  offered  sacrifices  to  the  moon.  The  opinion 
also  extensively  prevailed,  that  it  was  in  the  power  of 
witches,  by  their  spells  and  charms,  not  only  to  darken 
the  moon,  but  to  bring  her  down  from  her  orbit,  and 
to  compel  her  to  shed  her  baleful  influences  upon  the 
earth.  In  solar  eclipses,  also,  especially  when  total,  the 
sun  was  supposed  to  turn  away  his  face  in  abhorrence 
of  some  atrocious  crime,  that  either  had  been  perpetra- 
ted or  was  about  to  be  perpetrated,  and  to  threaten 


208  LETTERS  ON  ASTRONOMY. 

mankind  with  everlasting  night,  and  the  destruction  of 
the  world.  To  such  superstitions  Milton  alludes,  in  the 
passage  which  I  have  taken  for  the  motto  of  this  Letter. 
The  Chinese,  who,  from  a  very  high  period  of  an- 
tiquity, have  been  great  observers  of  eclipses,  although 
they  did  not  take  much  notice  of  those  of  the  moon, 
regarded  eclipses  of  the  sun  in  general  as  unfortunate, 
but  especially  such  as  occurred  on  the  first  day  of  the 
year.  These  were  thought  to  forebode  the  greatest  ca- 
lamities to  the  emperor,  who  on  such  occasions  did  not 
receive  the  usual  compliments  of  the  season.  When, 
from  the  predictions  of  their  astronomers,  an  eclipse 
of  the  sun  was  expected,  they  made  great  preparation 
at  court  for  observing  it ;  and  as  soon  as  it  commenc- 
ed, a  blind  man  beat  a  drum,  a  great  concourse  assem- 
bled, and  the  mandarins,  or  nobility,  appeared  in  state, 


LETTER  XIX. 

LONGITUDE. TIDES. 

"  First  in  his  east,  the  glorious  lamp  was  seen, 
Regent  of  day,  and  all  the  horizon  round 
Invested  with  bright  rays,  jocund  to  run 
His  longitude  through  heaven's  high  road  ;  the  gray 
Dawn  and  the  Pleiades  before  him  danced, 
Shedding  sweet  influence." — Milton. 

THE  ancients  studied  astronomy  chiefly  as  subsidiary 
to  astrology,  with  the  vain  hope  of  thus  penetrating  the 
veil  of  futurity,  and  reading  their  destinies  among  the 
stars.  The  moderns,  on  the  other  hand,  have  in  view, 
as  the  great  practical  object  of  this  study,  the  perfecting 
of  the  art  of  navigation.  When  we  reflect  on  the  vast 
interests  embarked  on  the  ocean,  both  of  property  and 
life,  and  upon  the  immense  benefits  that  accrue  to  soci- 
ety from  a  safe  and  speedy  intercourse  between  the 
different  nations  of  the  earth,  we  cannot  but  see  that 
whatever  tends  to  enable  the  mariner  to  find  his  way 
on  the  pathless  ocean,  and  to  secure  him  against  its 


LONGITUDE.  209 

multiplied  dangers,  must  confer  a  signal  benefit  on  so- 
ciety. 

In  ancient  times,  to  venture  out  of  sight  of  land  was 
deemed  an  act  of  extreme  audacity ;  and  Horace,  the 
Roman  poet,  pronounces  him  who  first  ventured  to  trust 
his  frail  bark  to  the  stormy  ocean,  endued  with  a  heart 
of  oak,  and  girt  with  triple  folds  of  brass.  But  now, 
the  navigator  who  fully  avails  himself  of  all  the  resour- 
ces of  science,  and  especially  of  astronomy,  may  launch 
fearlessly  on  the  deep,  and  almost  bid  defiance  to  rocks 
and  tempests.  By  enabling  the  navigator  to  find  his 
place  on  the  ocean  with  almost  absolute  precision,  how- 
ever he  may  have  been  driven  about  by  the  winds,  and 
however  long  he  may  have  been  out  of  sight  of  land, 
astronomers  must  be  held  as  great  benefactors  to  all 
who  commit  either  their  lives  or  their  fortunes  to  the 
the  sea.  Nor  have  they  secured  to  the  art  of  naviga- 
tion such  benefits  without  incredible  study  and  toil,  in 
watching  the  motions  of  the  heavenly  bodies,  in  inves- 
tigating the  laws  by  which  their  movements  are  gov- 
erned, and  in  reducing  all  their  discoveries  to  a  form 
easily  available  to  the  navigator,  so  that,  by  some  sim- 
ple observation  on  one  or  two  of  the  heavenly  bodies, 
with  instruments  which  the  astronomer  has  invented, 
and  prepared  for  his  use,  and  by  looking  out  a  few 
numbers  in  tables  which  have  been  compiled  for  him, 
with  immense  labor,  he  may  ascertain  the  exact  place 
he  occupies  on  the  surface  of  the  globe,  thousands  of 
miles  from  land. 

The  situation  of  any  place  is  known  by  its  latitude  and 
longitude.  As  charts  of  every  ocean  and  sea  are  fur- 
nished to  the  sailor,  in  which  are  laid  down  the  latitudes 
and  longitudes  of  every  point  of  land,  whether  on  the 
shores  of  islands  or  the  main,  he  has,  therefore,  only  to 
ascertain  his  latitude  and  longitude  at  any  particular 
place  on  the  ocean,  in  order  to  find  where  he  is,  with 
respect  to  the  nearest  point  of  land,  although  this  may 
be,  and  may  always  have  been,  entirely  out  of  sight  to 
him. 

18* 


210  LETTERS  ON  ASTRONOMY. 

To  determine  the  latitude  of  a  place  is  comparatively 
an  easy  matter,  whenever  we  can  see  either  the  sun  or 
the  stars.  The  distance  of  the  sun  from  the  zenith, 
when  on  the  meridian,  on  a  given  day  of  the  year, 
(which  distance  we  may  easily  take  with  the  sextant,) 
enables  us,  with  the  aid  of  the  tables,  to  find  the  lati- 
tude of  the  place ;  or,  by  taking  the  altitude  of  the 
north  star,  we  at  once  obtain  the  latitude. 

The  longitude  of  a  place  may  be  found  by  any 
method,  by  which  we  may  ascertain  how  much  its  time 
of  day  differs  from  that  of  Greenwich  at  the  same 
moment.  A  place  that  lies  eastward  of  another  comes 
to  the  meridian  an  hour  earlier  for  every  fifteen  degrees 
of  longitude,  and  of  course  has  the  hour  of  the  day  so 
much  in  advance  of  the  other,  so  that  it  counts  one 
o'clock  when  the  other  place  counts  twelve.  On  the 
other  hand,  a  place  lying  westward  of  another  comes 
to  the  meridian  later  by  one  hour  for  every  fifteen  de- 
grees, so  that  it  counts  only  eleven  o'clock  when  the 
other  place  counts  twelve.  Keeping  these  principles 
in  view,  it  is  easy  to  see  that  a  comparison  of  the  dif- 
ference of  time  between  two  places  at  the  same  mo- 
ment, allowing  fifteen  degrees  for  an  hour,  sixty  min- 
utes for  every  four  minutes  of  time,  and  sixty  seconds 
for  every  four  seconds  of  time,  affords  us  an  accurate 
mode  of  finding  the  difference  of  longitude  between 
the  two  places.  This  comparison  may  be  made  by 
means  of  a  chronometer,  or  from  solar  or  lunar  eclipses, 
or  by  what  is  called  the  lunar  method  of  finding  the 
longitude. 

Chronometers  are  distinguished  from  clocks,  by  be- 
ing regulated  by  means  of  a  balance-wheel  instead  of  a 
pendulum.  A  watch,  therefore,  comes  under  the  gen- 
eral definition  of  a  chronometer  ;  but  the  name  is  more 
commonly  applied  to  larger  time-pieces,  too  large  to  be 
carried  about  the  person,  and  constructed  with  the 
greatest  possible  accuracy,  with  special  reference  to 
finding  the  longitude.  Suppose,  then,  we  are  furnished 
with  a  chronometer  set  to  Greenwich  time.  We  arrive 


LONGITUDE. 

at  New  York,  for  example,  and  compare  it  with  the 
time  there.  We  find  it  is  five  hours  in  advance  of  the 
New-York  time,  indicating  five  o'clock,  P.  M.,  when  it 
is  noon  at  New  York.  Hence  we  find  that  the  lon- 
gitude of  New  York  is  5X15=75  degrees.*  The 
time  at  New  York,  or  any  individual  place,  can  be 
known  by  observations  with  the  transit-instrument, 
which  gives  us  the  precise  moment  when  the  sun  is 
on  the  meridian. 

It  would  not  be  necessary  to  resort  to  Greenwich, 
for  the  purpose  of  setting  our  chronometer  to  Green- 
wich time,  as  it  might  be  set  at  any  place  whose  lon- 
gitude is  known,  having  been  previously  determined. 
Thus,  if  we  know  that  the  longitude  of  a  certain  place 
is  exactly  sixty  degrees  east  of  Greenwich,  we  have 
only  to  set  our  chronometer  four  hours  behind  the 
time  at  that  place,  and  it  will  be  regulated  to  Green- 
wich time.  Hence  it  is  a  matter  of  the  greatest  im- 
portance to  navigation,  that  the  longitude  of  numerous 
ports,  in  different  parts  of  the  earth,  should  be  accu- 
rately determined,  so  that  when  a  ship  arrives  at  any 
such  port,  it  may  have  the  means  of  setting  or  verify- 
ing its  chronometer. 

This  method  of  taking  the  longitude  seems  so  easy, 
that  you  will  perhaps  ask,  why  it  is  not  sufficient  for  all 
purposes,  and  accordingly,  why  it  does  not  supersede 
the  more  complicated  and  laborious  methods?  why 
every  sailor  does  not  provide  himself  with  a  chronom- 
eter, instead  of  finding  his  longitude  at  sea  by  tedious 
and  oft-repeated  calculations,  as  he  is  in  the  habit  of 
doing?  I  answer,  it  is  only  in  a  few  extraordinary 
cases  that  chronometers  have  been  constructed  of  such 
accuracy  as  to  afford  results  as  exact  as  those  obtained 
by  the  other  methods,  to  be  described  shortly ;  and  in- 
struments of  such  perfection  are  too  expensive  for  gen- 
eral use  among  sailors.  Indeed,  the  more  common 
chronometers  cost  too  much  to  come  within  the  means 

*  The  exact  longitude  of  the  City  Hall,  in  the  city  of  New  York, 
is  4h.56m.33.5s. 


212  LETTERS  ON  ASTRONOMY. 

of  a  great  majority  of  sea-faring  men.  Moreover,  by 
being  transported  from  place  to  place,  chronometers 
are  liable  to  change  their  rate.  By  the  rate  of  any 
time-piece  is  meant  its  deviation  from  perfect  accuracy. 
Thus,  if  a  clock  should  gain  one  second  per  day,  one 
day  with  another,  and  we  should  find  it  impossible  to 
bring  it  nearer  to  the  truth,  we  may  reckon  this  as  its 
rate,  and  allow  for  it  in  our  estimate  of  the  time  of  any 
particular  observation.  If  the  error  was  not  uniform, 
but  sometimes  greater  and  sometimes  less  than  one 
second  per  day,  then  the  amount  of  such  deviation  is 
called  its  "  variation  from  its  mean  rate."  I  introduce 
these  minute  statements,  (which  are  more  precise  than 
I  usually  deem  necessary,)  to  show  you  to  what  an 
astonishing  degree  of  accuracy  chronometers  have  in 
some  instances  been  brought.  They  have  been  carried 
from  London  to  Baffin's  Bay,  and  brought  back,  after 
a  three  years'  voyage,  and  found  to  have  varied  from 
their  mean  rate,  during  the  whole  time,  only  a  second 
or  two,  while  the  extreme  variation  of  several  chronom- 
eters, tried  at  the  Royal  Observatory  at  Greenwich, 
never  exceeded  a  second  and  a  half.  Could  chronom- 
eters always  be  depended  on  to  such  a  degree  of  accu- 
racy as  this,  we  should  hardly  desire  any  thing  better 
for  determining  the  longitude  of  different  places  on  the 
earth.  A  recent  determination  of  the  longitude  of  the 
City  Hall  in  New  York,  by  means  of  three  chronom- 
eters, sent  out  from  London  expressly  for  that  purpose, 
did  not  differ  from  the  longitude  as  found  by  a  solar 
eclipse  (which  is  one  of  the  best  methods)  but  a  sec- 
ond and  a  quarter. 

Eclipses  of  the  sun  and  moon  furnish  the  means  of 
ascertaining  the  longitude  of  a  place,  because  the  en- 
trance of  the  moon  irto  the  earth's  shadow  in  a  lunar 
eclipse,  and  the  entrance  of  the  moon  upon  the  disk 
of  the  sun  in  a  solar  eclipse,  are  severally  examples  of 
one  of  those  instantaneous  occurrences  in  the  heavens, 
which  afford  the  means  of  comparing  the  times  of 
different  places,  and  of  thus  determining  their  differ- 


LONGITUDE.  213 

ences  of  longitude.  Thus,  if  the  commencement  of  a 
lunar  eclipse  was  seen  at  one  place  an  hour  sooner  than 
at  another,  the  two  places  would  be  fifteen  degrees 
apart,  in  longitude ;  and  if  the  longitude  of  one  of  the 
places  was  known,  that  of  the  other  would  become 
known  also.  The  exact  instant  of  the  moon's  entering 
into  the  shadow  of  the  earth,  however,  cannot  be  de- 
termined with  very  great  precision,  since  the  moon,  in 
passing  through  the  earth's  penumbra,  loses  its  light 
gradually,  so  that  the  moment  when  it  leaves  the  pe- 
numbra and  enters  into  the  shadow  cannot  be  very  ac- 
curately defined.  The  first  contact  of  the  moon  with 
the  sun's  disk,  in  a  solar  eclipse,  or  the  moment  of  leav- 
ing it, — that  is,  the  beginning  and  end  of  the  eclipse, — 
are  instants  that  can  be  determined  with  much  precis- 
ion, and  accordingly  they  are  much  relied  on  for  an 
accurate  determination  of  the  longitude.  But,  on  ac- 
count of  the  complicated  and  laborious  nature  of  the 
calculation  of  the  longitude  from  an  eclipse  of  the  sun, 
(since  the  beginning  and  end  are  not  seen  at  different 
places,  at  the  same  moment,)  this  method  of  finding 
the  longitude  is  not  adapted  to  common  use,  nor  avail- 
able at  sea.  It  is  useful,  however,  for  determining  the 
longitude  of  fixed  observatories.  The  lunar  method 
of  finding  the  longitude  is  the  most  refined  and  accu- 
rate of  all  the  modes  practised  at  sea.  The  motion 
of  the  moon  through  the  heavens  is  so  rapid,  that  she 
perceptibly  alters  her  distance  from  any  star  every  min- 
ute ;  consequently,  the  moment  when  that  distance  is  a 
certain  number  of  degrees  and  minutes  is  one  of  those 
instantaneous  events,  which  may  be  taken  advantage 
of  for  comparing  the  times  of  different  places,  and  thus 
determining  their  difference  of  longitude.  Now,  in  a 
work  called  the  '  Nautical  Almanac,'  printed  in  Lon- 
don, annually,  for  the  use  of  navigators,  the  distance 
of  the  moon  from  the  sun  by  day,  or  from  known  fixed 
stars  by  night,  for  every  day  and  night  in  the  year,  is 
calculated  beforehand.  If,  therefore,  a  sailor  wishes 
to  ascertain  his  longitude,  he  may  take  with  his  sextant 


214  LETTERS  ON  ASTRONOMY. 

the  distance  of  the  moon  from  one  of  these  stars  at 
any  time, — suppose  nine  o'clock,  at  night, — and  then 
turn  to  the  '  Nautical  Almanac,'  and  see  what  time 
it  was  at  Greenwich  when  the  distance  between  the 
moon  and  that  star  was  the  same.  Let  it  be  twelve 
o'clock,  or  three  hours  in  advance  of  his  time :  his 
longitude,  of  course,  is  forty-five  degrees  west. 

This  method  requires  more  skill  and  accuracy  than 
are  possessed  by  the  majority  of  seafaring  men  ;  but, 
when  practised  with  the  requisite  degree  of  skill,  its  re- 
sults are  very  satisfactory.  Captain  Basil  Hall,  one  of 
the  most  scientific  commanders  in  the  British  navy,  re- 
lates the  following  incident,  to  show  the  excellence  of 
this  method.  He  sailed  from  San  Bias,  on  the  west 
coast  of  Mexico,  and,  after  a  voyage  of  eight  thousand 
miles,  occupying  eighty-nine  days,  arrived  off  Rio  de 
Janeiro,  having,  in  this  interval,  passed  through  the 
Pacific  Ocean,  rounded  Cape  Horn,  and  crossed  the 
South  Atlantic,  without  making  any  land,  or  even  see- 
ing a  single  sail,  with  the  exception  of  an  American 
whaler  off  Cape  Horn.  When  within  a  week's  sail  of 
Rio,  he  set  seriously  about  determining,  by  lunar  obser- 
vations, the  precise  line  of  the  ship's  course,  and  its  sit- 
uation at  a  determinate  moment ;  and  having  ascertain- 
ed this  within  from  five  to  ten  miles,  ran  the  rest  of  the 
way  by  those  more  ready  and  compendious  methods, 
known  to  navigators,  which  can  be  safely  employed  for 
short  trips  between  one  known  point  and  another,  but 
which  cannot  be  trusted  in  long  voyages,  where  the 
moon  is  the  only  sure  guide.  They  steered  towards  Rio 
Janeiro  for  some  days  after  taking  the  lunars,  and,  hav- 
ing arrived  within  fifteen  or  twenty  miles  of  the  coast, 
they  hove  to,  at  four  in  the  morning,  till  the  day  should 
break,  and  then  bore  up,  proceeding  cautiously,  on  ac- 
count of  a  thick  fog  which  enveloped  them.  As  this 
cleared  away,  they  had  the  satisfaction  of  seeing  the 
great  Sugar-Loaf  Rock,  which  stands  on  one  side  of 
the  harbor's  mouth,  so  nearly  right  ahead,  that  they 
had  not  to  alter  their  course  above  a  point,  in  order  to 


LONGITUDE.  215 

hit  the  entrance  of  the  harbor.  This  was  the  first  land 
they  had  seen  for  three  months,  after  crossing  so  many 
seas,  and  being  set  backwards  arid  forwards  by  innu- 
merable currents  and  foul  winds.  The  effect  on  all  on 
board  was  electric ;  and  the  admiration  of  the  sailors 
was  unbounded.  Indeed,  what  could  be  more  admira- 
ble than  that  a  man  on  the  deck  of  a  vessel,  by  meas- 
uring the  distance  between  the  moon  and  a  star,  with 
a  little  instrument  which  he  held  in  his  hand,  could 
determine  his  exact  place  on  the  earth's  surface  in  the 
midst  of  a  vast  ocean,  after  having  traversed  it  in  all 
directions,  for  three  months,  crossing  his  track  many 
times,  and  all  the  while  out  of  sight  of  land  ? 

The  lunar  method  of  finding  the  longitude  could 
never  have  been  susceptible  of  sufficient  accuracy,  had 
not  the  motions  of  the  moon,  with  all  their  irregular- 
ities, been  studied  and  investigated  by  the  most  labo- 
rious and  profound  researches.  Hence  Newton,  while 
wrapt  in  those  meditations  which,  to  superficial  minds, 
would  perhaps  have  appeared  rather  curious  than  use- 
ful, inasmuch  as  they  respected  distant  bodies  of  the 
universe  which  seemed  to  have  little  connexion  with 
the  affairs  of  this  world,  was  laboring  night  and  day  for 
the  benefit  of  the  sailor  and  the  merchant.  He  was 
guiding  the  vessel  of  the  one,  and  securing  the  mer- 
chandise of  the  other  ;  and  thus  he  contributed  a  large 
share  to  promote  the  happiness  of  his  fellow-men,  not 
only  in  exalting  the  powers  of  the  human  intellect,  but 
also  in  preserving  the  lives  and  fortunes  of  those  en- 
gaged in  navigation  and  commerce.  Principles  in  sci- 
ence are  rules  in  art ;  and  the  philosopher  who  is  en- 
gaged in  the  investigation  of  these  principles,  although 
his  pursuits  may  be  thought  less  practically  useful  than 
those  of  the  artisan  who  carries  out  those  principles 
into  real  life,  yet,  without  the  knowledge  of  the  prin- 
ciples, the  rules  would  have  never  been  known.  Stud- 
ies, therefore,  the  most  abstruse,  are,  when  viewed  as 
furnishing  rules  to  act,  often  productive  of  the  highest 
practical  utility. 


LETTERS  ON  ASTRONOMY. 

Since  the  tides  are  occasioned  by  the  influence  of 
the  sun  and  moon,  I  will  conclude  this  Letter  with  a 
few  remarks  on  this  curious  phenomenon.  By  the  tides 
are  meant  the  alternate  rising  and  falling  of  the  waters 
of  the  ocean.  Its  greatest  and  least  elevations  are 
called  high  and  low  water ;  its  rising  and  falling  are 
called  flood  and  ebb  ;  and  the  extraordinary  high  and 
low  tides  that  occur  twice  every  month  are  called  spring 
and  neap  tides.  It  is  high  or  low  tide  on  opposite 
sides  of  the  globe  at  the  same  time.  If,  for  example, 
we  have  high  water  at  noon,  it  is  also  high  water  to 
those  who  live  on  the  meridian  below  us,  where  it  is 
midnight.  In  like  manner,  low  water  occurs  simultane- 
ously on  opposite  sides  of  the  meridian.  The  average 
amount  of  the  tides  for  the  whole  globe  is  about  two  and 
a  half  feet ;  but  their  actual  height  at  different  places 
is  very  various,  sometimes  being  scarcely  perceptible, 
and  sometimes  rising  to  sixty  or  seventy  feet.  At  the 
same  place,  also,  the  phenomena  of  the  tides  are  very 
different  at  different  times.  In  the  Bay  of  Fundy. 
where  the  tide  rises  seventy  feet,  it  comes  in  a  mighty 
wave,  seen  thirty  miles  off,  and  roaring  with  a  loud 
noise.  At  the  mouth  of  the  Severn,  in  England,  the 
flood  comes  up  in  one  head  about  ten  feet  high,  bring- 
ing certain  destruction  to  any  small  craft  that  has  been 
unfortunately  left  by  the  ebbing  waters  on  the  flats  ; 
and  as  it  passes  the  mouth  of  the  Avon,  it  sends  up 
that  small  river  a  vast  body  of  water,  rising,  at  Bristol, 
forty  or  fifty  feet. 

Tides  are  caused  by  the  unequal  attractions  of  the 
sun  and  moon  upon  different  parts  of  the  earth.  Sup- 
pose the  projectile  force  by  which  the  earth  is  carried 
forward  in  her  orbit  to  be  suspended,  and  the  earth  to 
fall  towards  one  of  these  bodies, — the  moon,  for  exam- 
ple,— in  consequence  of  their  mutual  attraction.  Then, 
if  all  parts  of  the  earth  fell  equally  towards  the  moon, 
no  derangement  of  its  different  parts  would  result,  any 
more  than  of  the  particles  of  a  drop  of  water,  in  its  de- 
scent to  the  ground.  But  if  one  part  fell  faster  than 


TIDES.  217 

another,  the  different  portions  would  evidently  be  sep- 
arated from  each  other.  Now,  this  is  precisely  what 
takes  place  with  respect  to  the  earth,  in  its  fall  towards 
the  moon.  The  portions  of  the  earth  in  the  hemis- 
phere next  to  the  moon,  on  account  of  being  nearer  to 
the  centre  of  attraction,  fall  faster  than  those  in  the 
opposite  hemisphere,  and  consequently  leave  them  be- 
hind. The  solid  earth,  on  account  of  its  cohesion,  can- 
not obey  this  impulse,  since  all  its  different  portions 
constitute  one  mass,  which  is  acted  on  in  the  same 
manner  as  though  it  were  all  collected  in  the  centre ; 
but  the  waters  on  the  surface,  moving  freely  under 
this  impulse,  endeavor  to  desert  the  solid  mass  and  fall 
towards  the  moon.  For  a  similar  reason,  the  waters  in 
the  opposite  hemisphere,  falling  less  towards  the  moon 
than  the  solid  earth  does,  are  left  behind,  or  appear  to 
rise. 

But  if  the  moon  draws  the  waters  of  the  earth  into 
an  oval  form  towards  herself,  raising  them  simultane- 
ously on  the  opposite  sides  of  the  earth,  they  must  ob- 
viously be  drawn  away  from  the  intermediate  parts  of 
the  earth,  where  it  must  at  the  same  time  be  low  water. 

Fig.  46. 


Thus,  in  Fig.  46,  the  moon,  M,  raises  the  waters  be- 
neath itself  at  Z  and  N,  at  which  places  it  is  high  wa- 
19  L.  A. 


218  LETTERS  ON  ASTRONOMY. 

ter,  but  at  the  same  time  depresses  the  waters  at  H  and 
R,  at  which  places  it  is  low  water.  Hence,  the  inter- 
val between  the  high  and  low  tide,  on  successive  days, 
is  about  fifty  minutes,  corresponding  to  the  progress  of 
the  moon  in  her  orbit  from  west  to  east,  which  causes 
her  to  come  to  the  meridian  about  fifty  minutes  later 
every  day.  There  occurs,  however,  an  intermediate 
tide,  when  the  moon  is  on  the  lower  meridian,  so  that 
the  interval  between  two  high  tides  is  about  twelve 
hours,  and  twenty-five  minutes. 

Were  it  not  for  the  impediments  which  prevent  the 
force  from  producing  its  full  effects,  we  might  expect 
to  see  the  great  tide- wave,  as  the  elevated  crest  is 
called,  always  directly  beneath  the  moon,  attending  it 
regularly  around  the  globe.  But  the  inertia  of  the 
waters  prevents  their  instantly  obeying  the  moon's  at- 
traction, and  the  friction  of  the  waters  on  the  bottom 
of  the  ocean  still  further  retards  its  progress.  It  is 
not,  therefore,  until  several  hours  (differing  at  different 
places)  after  the  moon  has  passed  the  meridian  of  a 
place,  that  it  is  high  tide  at  that  place. 

The  sun  has  an  action  similar  to  that  of  the  moon, 
but  only  one  third  as  great.  On  account  of  the  great 
mass  of  the  sun,  compared  with  that  of  the  moon,  we 
might  suppose  that  his  action  in  raising  the  tides  would 
be  greater  than  the  moon's ;  but  the  nearness  of  the 
moon  to  the  earth  more  than  compensates  for  the  sun's 
greater  quantity  of  matter.  As,  however,  wrong  views 
are  frequently  entertained  on  this  subject,  let  us  en- 
deavor to  form  a  correct  idea  of  the  advantage  which 
the  moon  derives  from  her  proximity.  It  is  not  that 
her  actual  amount  of  attraction  is  thus  rendered  great- 
er than  that  of  the  sun  ;  but  it  is  that  her  attraction  for 
the  different  parts  of  the  earth  is  very  unequal,  while 
that  of  the  sun  is  nearly  uniform.  It  is  the  inequality 
of  this  action,  and  not  the  absolute  force,  that  produces 
the  tides.  The  sun  being  ninety-five  millions  of  miles 
from  the  earth,  while  the  diameter  of  the  earth  is  only 
one  twelve  thousandth  part  of  this  distance,  the  effects 


TIDES.  219 

of  the  sun's  attraction  will  be  nearly  the  same  on  all 
parts  of  the  earth,  and  therefore  will  not,  as  was  ex- 
plained of  the  moon,  tend  to  separate  the  waters  from 
the  earth  on  the  nearest  side,  or  the  earth  from  the  wa- 
ters on  the  remotest  side,  but  in  a  degree  proportional- 
ly smaller.  But  the  diameter  of  the  earth  is  one  thir- 
tieth the  distance  of  the  moon,  and  therefore  the  moon 
acts  with  considerably  greater  power  on  one  part  of  the 
earth  than  on  another. 

As  the  sun  and  moon  both  contribute  to  produce  the 
tides,  and  as  they  sometimes  act  together  and  some- 
times in  opposition  to  each  other,  so  corresponding  va- 
riations occur  in  the  height  of  the  tide.  The  spring 
tides,  or  those  which  rise  to  an  unusual  height  twice  a 
month,  are  produced  by  the  sun  and  moon's  acting  to- 
gether ;  and  the  neap  tides,  or  those  which  are  unus- 
ually low  twice  a  month,  are  produced  by  the  sun  and 
moon's  acting  in  opposition  to  each  other.  The  spring 
tides  occur  at  the  syzygies :  the  neap  tides  at  the  quad- 
ratures. At  the  time  of  new  moon,  the  sun  and  moon 
both  being  on  the  same  side  of  the  earth,  and  acting 
upon  it  in  the  same  line,  their  actions  conspire,  and  the 
sun  may  be  considered  as  adding  so  much  to  the  force 
of  the  moon.  We  have  already  seen  how  the  moon 
contributes  to  raise  a  tide  on  the  opposite  side  of  the 
earth.  But  the  sun,  as  well  as  the  moon,  raises  its  own 
tide-wave,  which  at  new  moon  coincides  with  the  lu- 
nar tide-wave.  This  will  be  plain  on  inspecting  the  di- 
agram, Fig.  47,  on  page  220,  where  S  represents  the  sun, 
C,  the  moon  in  conjunction,  O,  the  moon  in  opposition, 
and  Z,  N,  the  tide-wave.  Since  the  sun  and  moon 
severally  raise  a  tide- wave,  and  the  two  here  coincide, 
it  is  evident  that  a  peculiarly  high  tide  must  occur 
when  the  two  bodies  are  in  conjunction,  or  at  new 
moon.  At  full  moon,  also,  the  two  luminaries  conspire 
in  the  same  way  to  raise  the  tide ;  for  we  must  recol- 
lect that  each  body  contributes  to  raise  a  tide  on  the 
opposite  side.  Thus,  when  the  sun  is  at  S  and  the 
moon  at  O,  the  sun  draws  the  waters  on  the  side  next 


220  LETTERS  ON  ASTRONOMY. 

Fig.  47. 


to  it  away  from  the  earth,  and  the  moon  draws  the 
earth  away  from  the  waters  on  that  side ;  their  united 
actions,  therefore,  conspire,  and  an  unusually  high  tide 
is  the  result.  On  the  side  next  to  O,  the  two  forces 
likewise  conspire :  for  while  the  moon  draws  the  wa- 
ters away  from  the  earth,  the  sun  draws  the  earth  away 
from  the  waters.  In  both  cases  an  unusually  low  tide 
is  produced ;  for  the  more  the  water  is  elevated  at  Z 
and  N,  the  more  it  will  be  depressed  at  H  and  R,  the 
places  of  low  tide. 

Twice  a  month,  also,  namely,  at  the  quadratures  of 
the  moon,  the  tides  neither  rise  so  high  nor  fall  so  low 
as  at  other  times,  because  then  the  sun  and  moon  act 
against  each  other.  Thus,  in  Fig.  48,  while  F  tends 
to  raise  the  water  at  Z,  S  tends  to  depress  it,  and 
consequently  the  high  tide  is  less  than  usual.  Again, 
while  F  tends  to  depress  the  water  at  R,  S  tends  to 
elevate  it.  and  therefore  the  low  tide  is  less  than  usual. 
Hence  the  difference  between  high  and  low  water  is 
only  half  as  great  at  neap  as  at  spring  tide.  In  the 
diagrams,  the  elevation  and  depression  of  the  waters  is 
represented,  for  the  sake  of  illustration,  as  far  greater 


TIDES.  221 

Fig.  48. 


than  it  really  is  ;  for  you  must  recollect  that  the  aver- 
age height  of  the  tides  for  the  whole  globe  is  only 
about  two  and  a  half  feet,  a  quantity  so  small,  in  com- 
parison with  the  diameter  of  the  earth,  that  were  the 
due  proportions  preserved  in  the  figures,  the  effect 
would  be  wholly  insensible. 

The  variations  of  distance  in  the  sun  are  not  great 
enough  to  influence  the  tides  very  materially,  but  the 
variations  in  the  moon's  distances  have  a  striking  effect. 
The  tides  which  happen,  when  the  moon  is  in  perigee, 
are  considerably  greater  than  when  she  is  in  apogee ; 
and  if  she  happens  to  be  in  perigee  at  the  time  of  the 
syzygies,  the  spring  tides  are  unusually  high. 

The  motion  of  the  tide-wave  is  not  a  progressive  mo- 
tion, but  a  mere  undulation,  and  is  to  be  carefully  dis- 
tinguished from  the  currents  to  which  it  gives  rise.  If 
the  ocean  completely  covered  the  earth,  the  sun  and 
moon  being  in  the  equator,  the  tide-wave  would  travel 
at  the  same  rate  as  the  earth  revolves  on  its  axis.  In- 
deed, the  correct  way  of  conceiving  of  the  tide-wave, 
is  to  consider  the  moon  at  rest,  and  the  earth,  in  its  ro- 
tation from  west  to  east,  as  bringing  successive  portions 
19* 


222  LETTERS  ON  ASTRONOMY. 

of  water  under  the  moon,  which  portions  being  eleva- 
ted successively,  at  the  same  rate  as  the  earth  revolves 
on  its  axis,  have  a  relative  motion  westward,  at  the 
same  rate. 

The  tides  of  rivers,  narrow  bays,  and  shores  far  from 
the  main  body  of  the  ocean,  are  not  produced  in  those 
places  by  the  direct  action  of  the  sun  and  moon,  but 
are  subordinate  waves  propagated  from  the  great  tide- 
wave,  and  are  called  derivative  tides,  while  those  raised 
directly  by  the  sun  and  moon  are  called  primitive 
tides. 

The  velocity  with  which  the  tide  moves  will  depend 
on  various  circumstances,  but  principally  on  the  depth, 
and  probably  on  the  regularity,  of  the  channel.  If  the 
depth  is  nearly  uniform  the  tides  will  be  regular ;  but 
if  some  parts  of  the  channel  are  deep  while  others  are 
shallow,  the  waters  will  be  detained  by  the  greater  fric- 
tion of  the  shallow  places,  and  the  tides  will  be  irregu- 
lar. The  direction,  also,  of  the  derivative  tide  may  be 
totally  different  from  that  of  the  primitive.  Thus,  in 
Fig.  49,  if  the  great  tide-wave,  moving  from  east  to 

Fig.  49. 


west,  is  represented  by  the  lines  1,  2,  3,  4,  the  deriva- 
tive tide,  which  is  propagated  up  a  river  or  bay,  will 


TIDES.  223 

be  represented  by  the  lines  3,  4,  5,  6,  7.  Advancing 
faster  in  the  channel  than  next  the  bank,  the  tides  will 
lag  behind  towards  the  shores,  and  the  tide-wave  will 
take  the  form  of  curves,  as  represented  in  the  diagram. 

On  account  of  the  retarding  influence  of  shoals,  and 
an  uneven,  indented  coast,  the  tide-wave  travels  more 
slowly  along  the  shores  of  an  island  than  in  the  neigh- 
boring sea,  assuming  convex  figures  at  a  little  distance 
from  the  island,  and  on  opposite  sides  of  it.  These  con- 
vex lines  sometimes  meet,  and  become  blended  in  such 
a  way,  as  to  create  singular  anomalies  in  a  sea  much 
broken  by  islands,  as  well  as  on  coasts  indented  with 
numerous  bays  and  rivers.  Peculiar  phenomena  are 
also  produced,  when  the  tide  flows  in  at  opposite  ex- 
tremities of  a  reef  or  island,  as  into  the  two  opposite 
ends  of  Long-Island  Sound.  In  certain  cases,  a  tide- 
wave  is  forced  into  a  narrow  arm  of  the  sea,  and  pro- 
duces very  remarkable  tides.  The  tides  of  the  Bay  of 
Fundy  (the  highest  in  the  world)  are  ascribed  to  this 
cause.  The  tides  on  the  coast  of  North  America  are 
derived  from  the  great  tide-wave  of  the  South  Atlantic, 
which  runs  steadily  northward  along  the  coast  to  the 
mouth  of  the  Bay  of  Fundy,  where  it  meets  the  north- 
ern tide-wave  flowing  in  the  opposite  direction.  This 
accumulated  wave  being  forced  into  the  narrow  space 
occupied  by  the  Bay,  produces  the  remarkable  tide  of 
that  place. 

The  largest  lakes  and  inland  seas  have  no  percepti- 
ble tides.  This  is  asserted  by  all  writers  respecting 
the  Caspian  and  Euxine ;  and  the  same  is  found  to  be 
true  of  the  largest  of  the  North- American  lakes,  Lake 
Superior.  Although  these  several  tracts  of  water  ap- 
pear large,  when  taken  by  themselves,  yet  they  occupy 
but  small  portions  of  the  surface  of  the  globe,  as  will 
appear  evident  from  the  delineation  of  them  on  the 
artificial  globe.  Now,  we  must  recollect  that  the  prim- 
itive tides  are  produced  by  the  unequal  action  of  the 
sun  and  moon  upon  the  different  parts  of  the  earth ; 
and  that  it  is  only  at  points  whose  distance  from  each 


224  LETTERS  ON  ASTRONOMY. 

other  bears  a  considerable  ratio  to  the  whole  distance 
of  the  sun  or  moon,  that  the  inequality  of  action  be- 
comes manifest.  The  space  required  to  make  the  ef- 
fect sensible  is  larger  than  either  of  these  tracts  of  wa- 
ter. It  is  obvious,  also,  that  they  have  no  opportunity 
to  be  subject  to  a  derivative  tide. 

Although  all  must  admit  that  the  tides  have  some 
connexion  with  the  sun  and  the  moon,  yet  there  are  so 
many  seeming  anomalies,  which  at  first  appear  irrecon- 
cilable with  the  theory  of  gravitation,  that  some  are  un- 
willing to  admit  the  explanation  given  by  this  theory. 
Thus,  the  height  of  the  tide  is  so  various,  that  at  some 
places  on  the  earth  there  is  scarcely  any  tide  at  all, 
while  at  other  places  it  rises  to  seventy  feet.  The  time 
of  occurrence  is  also  at  many  places  wholly  unconform- 
able  to  the  motions  of  the  moon,  as  is  required  by  the 
theory,  being  low  water  where  it  should  be  high  water  ; 
or,  instead  of  appearing  just  beneath  the  moon,  as  the 
theory  would  lead  us  to  expect,  following  it  at  the  dis- 
tance of  six,  ten,  or  even  fifteen,  hours  ;  and  finally,  the 
moon  sometimes  appears  to  have  no  part  at  all  in  pro- 
ducing the  tide,  but  it  happens  uniformly  at  noon  and 
midnight,  (as  is  said  to  be  the  case  at  the  Society  Isl- 
ands,) and  therefore  seems  wholly  dependent  on  the  sun. 

Notwithstanding  these  seeming  inconsistencies  with 
the  law  of  universal  gravitation,  to  which  the  explana- 
tion of  the  tides  is  referred,  the  correspondence  of  the 
tides  to  the  motions  of  the  sun  and  moon,  in  obedience 
to  the  law  of  attraction,  is  in  general  such  as  to  warrant 
the  application  of  that  law  to  them,  while  in  a  great 
majority  of  the  cases  which  appear  to  be  exceptions  to 
the  operation  of  that  law,  local  causes  and  impediments 
have  been  discovered,  which  modified  or  overruled  the 
uniform  operation  of  the  law  of  gravitation.  Thus  it 
does  not  disprove  the  reality  of  the  existence  of  a  force 
which  carries  bodies  near  the  surface  of  the  earth  tow- 
ards its  centre,  that  we  see  them  sometimes  compelled, 
by  the  operation  of  local  causes,  to  move  in  the  oppo- 
site direction.  A  ball  shot  from  a  cannon  is  still  subject 


PLANETS.  225 

to  the  law  of  gravitation,  although,  for  a  certain  time,  in 
obedience  to  the  impulse  given  it,  it  may  proceed  in  a 
line  contrary  to  that  in  which  gravity  alone  would  car- 
ry it.  The  fact  that  water  may  be  made  to  run  up  hill 
does  not  disprove  the  fact  that  it  usually  runs  down 
hill  by  the  force  of  gravity,  or  that  it  is  still  subject  to 
this  force,  although,  from  the  action  of  modifying  or 
superior  forces,  it  may  be  proceeding  in  a  direction  con- 
trary to  that  given  by  gravity.  Indeed,  those  who  have 
studied  the  doctrine  of  the  tides  most  profoundly  con- 
sider them  as  affording  a  striking  and  palpable  exhibi- 
tion of  the  truth  of  the  doctrine  of  universal  gravitation. 


LETTER  XX. 

PLANETS. MERCURY  AND  VENUS. 

"  First,  Mercury,  amidst  full  tides  of  light, 
Rolls  next  the  sun,  through  his  small  circle  bright; 
Our  earth  would  blaze  beneath  so  fierce  a  ray, 
And  all  its  marble  mountains  melt  away. 
Fair  Venus  next  fulfils  her  larger  round, 
With  softer  beams,  and  milder  glory  crowned  ; 
Friend  to  mankind,  she  glitters  from  afar, 
Now  the  bright  evening,  now  the  morning,  star." — Baker. 

THERE  is  no  study  in  which  more  is  to  be  hoped  for 
from  a  lucid  arrangement,  than  in  the  study  of  astrono- 
my. Some  subjects  involved  in  this  study  appear  very 
difficult  and  perplexing  to  the  learner,  before  he  has 
fully  learned  the  doctrine  of  the  sphere,  and  gained  a 
certain  familiarity  with  astronomical  doctrines,  which 
would  seem  very  easy  to  him  after  he  had  made  such 
attainments.  Such  an  order  ought  to  be  observed,  as 
shall  bring  out  the  facts  and  doctrines  of  the  science 
just  in  the  place  where  the  mind  of  the  learner  is  pre- 
pared to  receive  them.  Some  writers  on  astronomy 
introduce  their  readers  at  once  to  the  most  perplexing 
part  of  the  whole  subject, — the  planetary  motions.  I 
have  thought  a  different  course  advisable,  and  have 
therefore  commenced  these  Letters  with  an  account  of 


226  LETTERS  ON  ASTRONOMY. 

those  bodies  which  are  most  familiarly  known  to  us,  the 
earth,  the  sun,  and  the  moon.  In  connexion  with  the 
earth,  we  are  able  to  acquire  a  good  knowledge  of  the 
artificial  divisions  and  points  of  reference  that  are  es- 
tablished on  the  earth  and  in  the  heavens,  constituting 
the  doctrine  of  the  sphere.  You  thus  became  familiar 
with  many  terms  and  definitions  which  are  used  in  as- 
tronomy. These  ought  to  be  always  very  clearly  borne 
in  mind ;  and  if  you  now  meet  with  any  term,  the  defi- 
nition of  which  you  have  either  partially  or  wholly  for- 
gotten, let  me  strongly  recommend  to  you,  to  turn  back 
and  review  it,  until  it  becomes  as  familiar  to  you  as 
household  words.  Indeed,  you  will  find  it  much  to 
your  advantage  to  go  back  frequently,  and  reiterate 
the  earlier  parts  of  the  subject,  before  you  advance  to 
subjects  of  a  more  intricate  nature.  If  this  process 
should  appear  to  you  a  little  tedious,  still  you  will  find 
yourself  fully  compensated  by  the  clear  light  in  which 
all  the  succeeding  subjects  will  appear.  This  clear  and 
distinct  perception  of  the  ground  we  have  been  over 
shows  us  just  where  we  are  on  our  journey,  and  helps  us 
to  find  the  remainder  of  the  way  with  far  greater  ease 
than  we  could  otherwise  do.  I  do  not,  however,  pro- 
pose by  any  devices  to  relieve  you  from  the  trouble 
of  thinking.  Those  who  are  not  willing  to  incur  this 
trouble  can  never  learn  much  of  astronomy. 

In  introducing  you  to  the  planets,  (which  next  claim 
our  attention,)  I  will,  in  the  first  place,  endeavor  to 
convey  to  you  some  clear  views  of  these  bodies  indi- 
vidually, and  afterwards  help  you  to  form  as  correct  a 
notion  as  possible  of  their  motions  and  mutual  relations. 

The  name  planet  is  derived  from  a  Greek  word, 
(7tlavrjirjz,planetes,}  which  signifies  a  wanderer,  and  is 
applied  to  this  class  of  bodies,  because  they  shift  their 
positions  in  the  heavens,  whereas  the  fixed  stars  con- 
stantly maintain  the  same  places  with  respect  to  each 
other.  The  planets  known  from  a  high  antiquity  are, 
Mercury,  Venus,  Earth,  Mars,  Jupiter,  and  Saturn.  To 
these,  in  1781,  was  added  Uranus,  (or  Herschel,  as  it 


PLANETS.  227 

is  sometimes  called,  from  the  name  of  its  discoverer ;) 
and,  as  late  as  the  commencement  of  the  present  cen- 
tury, four  more  were  added,  namely,  Ceres,  Pallas,  Ju- 
no, and  Vesta.  These  bodies  are  designated  by  the 
following  characters  : 

1.  Mercury,  £  7.  Ceres,     ^ 

2.  Venus,  9  8.  Pallas,     $ 

3.  Earth,  ®  9.  Jupiter,  ^ 

4.  Mars,  ^  10.  Saturn,  \ 

5.  Vesta,  jj  11.  Uranus,  $ 

6.  Juno,  5 

The  foregoing  are  called  the  primary  planets.  Sev- 
eral of  these  have  one  or  more  attendants,  or  satellites, 
which  revolve  around  them  as  they  revolve  around  the 
sun.  The  Earth  has  one  satellite,  namely,  the  Moon ; 
Jupiter  has  four ;  Saturn,  seven ;  and  Uranus,  six. 
These  bodies  are  also  planets,  but,  in  distinction  from 
the  others,  they  are  called  secondary  planets.  Hence, 
the  whole  number  of  planets  are  twenty-nine,  namely, 
eleven  primary,  and  eighteen  secondary,  planets. 

You  need  never  look  for  a  planet  either  very  far  in 
the  north  or  very  far  in  the  south,  since  they  are  al- 
ways near  the  ecliptic.  Mercury,  which  deviates  fur- 
thest from  that  great  circle,  never  is  seen  more  than 
seven  degrees  from  it ;  and  you  will  hardly  ever  see 
one  of  the  planets  so  far  from  it  as  this,  but  they  all 
pursue  nearly  the  same  great  route  through  the  skies, 
in  their  revolutions  around  the  sun.  The  new  planets, 
however,  make  wider  excursions  from  the  plane  of  the 
ecliptic,  amounting,  in  the  case  of  Pallas,  to  thirty-four 
and  a  half  degrees. 

Mercury  and  Venus  are  called  inferior  planets,  be- 
cause they  have  their  orbits  nearer  to  the  sun  than  that 
of  the  earth ;  while  all  the  others,  being  more  distant 
from  the  sun  than  the  earth,  are  called  superior  plan- 
ets. The  planets  present  great  diversities  among  them- 
selves, in  respect  to  distance  from  the  sun,  magnitude, 
time  of  revolution,  and  density.  They  differ,  also,  in 


228  LETTERS   ON  ASTRONOMY. 

regard  to  satellites,  of  which,  as  we  have  seen,  three 
have  respectively  four,  six,  and  seven,  while  more  than 
half  have  none  at  all.  It  will  aid  the  memory,  and  ren- 
der our  view  of  the  planetary  system  more  clear  and  com- 
prehensive, if  we  classify,  as  far  as  possible,  the  various 
particulars  comprehended  under  the  foregoing  heads. 
As  you  have  had  an  opportunity,  in  preceding  Let- 
ters, of  learning  something  respecting  the  means  which 
astronomers  have  of  ascertaining  the  distances  and  mag- 
nitudes of  these  bodies,  you  will  not  doubt  that  they 
are  really  as  great  as  they  are  represented ;  but  when 
you  attempt  to  conceive  of  spaces  so  vast,  you  will  find 
the  mind  wholly  inadequate  to  the  task.  It  is  indeed 
but  a  comparatively  small  space  that  we  can  fully  com- 
prehend at  one  grasp.  Still,  by  continual  and  repeat- 
ed efforts,  we  may,  from  time  to  time,  somewhat  enlarge 
the  boundaries  of  our  mental  vision.  Let  us  begin 
with  some  known  and  familiar  space,  as  the  distance 
between  two  places  we  are  accustomed  to  traverse. 
Suppose  this  to  be  one  hundred  miles.  Taking  this  as 
our  measure,  let  us  apply  it  to  some  greater  distance, 
as  that  across  the  Atlantic  Ocean, — say  three  thousand 
miles.  From  this  step  we  may  advance  to  some  faint 
conception  of  the  diameter  of  the  earth ;  and  taking 
that  as  a  new  measure,  we  may  apply  it  to  such  greater 
spaces  as  the  distance  of  the  planets  from  the  sun.  I 
hope  you  will  make  trial  of  this  method  on  the  follow- 
ing comparative  statements  respecting  the  planets. 

Distances  from  the  Sun,  in  miles. 

I.  Mercury,    37,000,000  6.  Juno,      ) 

-2.  Venus,        68,000,000  7.  Ceres,     V    261,000,000 

3.  Earth,         95,000,000  8.  Pallas,    ) 

4.  Mars,         142,000,000  9.  Jupiter,       485,000,000 

5.  Vesta,       225,000,000  10.  Saturn,       890,000,000 

11.  Uranus,  or  Herschel,      1800,000,000 

The  dimensions  of  the  planetary  system  are  seen 
from  this  table  to  be  vast,  comprehending  a  circular 


PLANETS.  229 

space  thirty-six  hundred  millions  of  miles  in  diameter. 
A  rail-way  car,  travelling  constantly  at  the  rate  of  twen- 
ty miles  an  hour,  would  require  more  than  twenty 
thousand  years  to  cross  the  orbit  of  Uranus. 

Magnitudes. 

Diam.  in  miles.  Diam.  in  miles. 

1.  Mercury,      3140         5.  Ceres,  160 

2.  Venus,         7700         6.  Jupiter,  89,000 

3.  Earth,  7912         7.  Saturn,   79,000 

4.  Mars,  4200         8.  Uranus,  35,000 
We  remark  here  a  great  diversity  in  regard  to  mag- 
nitude,— a  diversity  which  does  not  appear  to  be  sub- 
ject to  any  definite  law.     While  Venus,  an   inferior 
planet,  is  nine  tenths  as  large  as  the  earth,  Mars,  a 
superior  planet,  is  only  one  seventh,  while  Jupiter  is 
twelve  hundred  and  eighty-one  times  as  large.     Al- 
though several  of  the    planets,  when   nearest  to   us, 
appear  brilliant  and  large,  when  compared  with  most 
of  the  fixed  stars,  yet  the  angle  which  they  subtend  is 
very  small, — that  of  Venus,  the  greatest  of  all,  never 
exceeding  about  one  minute,  which  is  less  than  one 
thirtieth  the  apparent  diameter  of  the  sun  or  moon, 
Jupiter,    also,    by  his   superior   brightness,   sometimes 
makes  a  striking  figure  among  the  stars  ;  yet  his  great- 
est apparent  diameter  is  less  than  one  fortieth  that  of 
the  sun. 

Periodic  Times. 

Mercury  revolves  around  the  sun  in  nearly  3  months. 
Venus,          "  "  "  "       7J      " 

Earth,  "  "  «  «       1     year. 

Mars,  "  «  "  «       2     years. 

Ceres,  "  "  "  "       4|      " 

Jupiter,        "  "  «  "     12        « 

Saturn,         "  "  "  "     29        " 

Uranus,        "  "  "  "     84        " 

From  this  view,  it  appears  that  the  planets  nearest 
the  sun  move  most  rapidly.     Thus,  Mercury  performs 

20  L.  A. 


230  LETTERS  ON  ASTRONOMY, 

nearly  three  hundred  and  fifty  revolutions  while  Ura- 
nus performs  one.  The  apparent  progress  of  the  most 
distant  planets  around  the  sun  is  exceedingly  slow. 
Uranus  advances  only  a  little  more  than  four  degrees 
in  a  whole  year ;  so  that  we  find  this  planet  occupying 
the  same  sign,  and  of  course  remaining  nearly  in  the 
same  part  of  the  heavens,  for  several  years  in  succes- 
sion. 

After  this  comparative  view  of  the  planets  in  gener- 
al, let  us  now  look  at  them  individually  ;  and  first,  of 
the  inferior  planets,  Mercury  and  Venus. 

MERCURY  and  VENUS,  having  their  orbits  so  far  with- 
in that  of  the  earth,  appear  to  us  as  attendants  upon 
the  sun.  Mercury  never  appears  further  from  the  sun 
than  twenty-nine  degrees,  and  seldom  so  far  ;  and  Ve- 
nus, never  more  than  about  forty-seven  degrees.  Both 
planets,  therefore,  appear  either  in  the  west  soon  after 
sunset,  or  in  the  east  a  little  before  sunrise.  In  high 
latitudes,  where  the  twilight  is  long,  Mercury  can  sel- 
dom be  seen  with  the  naked  eye,  and  then  only  when 
its  angular  distance  from  the  sun  is  greatest.  Coper- 
nicus, the  great  Prussian  astronomer,  (who  first  dis- 
tinctly established  the  order  of  the  solar  system,  as  at 
present  received,)  lamented,  on  his  death-bed,  that  he 
had  never  been  able  to  obtain  a  sight  of  Mercury ; 
and  Delambre,  a  distinguished  astronomer  of  France, 
saw  it  but  twice.  In  our  latitude,  however,  we  may 
see  this  planet  for  several  evenings  and  mornings,  if 
we  will  watch  the  time  (as  usually  given  in  the  alma- 
nac) when  it  is  at  its  greatest  elongations  from  the  sun. 
It  will  not,  however,  remain  long  for  our  gaze,  but  will 
soon  run  back  to  the  sun.  The  reason  of  this  will  be 
readily  understood  from  the  following  diagram,  Fig. 
50.  Let  S  represent  the  sun,  E,  the  earth,  and  M,  N, 
Mercury  at  its  greatest  elongations  from  the  sun,  and 
O  Z  P,  a  portion  of  the  sky.  Then,  since  we  refer  all 
distant  bodies  to  the  same  concave  sphere  of  the  heav- 
ens, it  is  evident  that  we  should  see  the  sun  at  Z,  and 
Mercury  at  O,  when  at  its  greatest  eastern  elongation, 


MERCURY  AND  VENUS. 


231 


E 


and  at  P,  when  at  its  greatest  western  elongation ;  and 
while  passing  from  M  to  N  through  Q,,  it  would  appear 
to  describe  the  arc  O  P  ;  and  while  passing  from  N  to 
M  through  R,  it  would  appear  to  run  back  across  the 
sun  on  the  same  arc.  It  is  further  evident  that  it 
would  be  visible  only  when  at  or  near  one  of  its  great- 
est elongations  ;  being  at  all  other  times  so  near  the 
sun  as  to  be  lost  in  his  light. 

A  planet  is  said  to  be  in  conjunction  with  the  sun 
when  it  is  seen  in  the  same  part  of  the  heavens  with  the 
sun.  Mercury  and  Venus  have  each  two  conjunctions, 
the  inferior  and  the  superior  conjunction.  The  infe- 
rior conjunction  is  its  position  when  in  conjunction  on 
the  same  side  of  the  sun  with  the  earth,  as  at  Q,,  in  the 
figure  :  the  superior  conjunction  is  its  position  when  on 
the  side  of  the  sun  most  distant  from  the  earth,  as  at  R. 

The  time  which  a  planet  occupies  in  making  one 
entire  circuit  of  the  heavens,  from  any  star,  until  it 
comes  round  to  the  same  star  again,  is  called  its  side- 
real revolution.  The  period  occupied  by  a  planet  be- 
tween two  successive  conjunctions  with  the  earth  is 
called  its  synodical  revolution.  Both  the  planet  and 


232 


LETTERS  ON  ASTRONOMY. 


the  earth  being  in  motion,  the  time  of  the  sy nodical 
revolution  of  Mercury  or  Venus  exceeds  that  of  the  si- 
dereal ;  for  when  the  planet  comes  round  to  the  place 
where  it  before  overtook  the  earth,  it  does  not  find  the 
earth  at  that  point,  but  far  in  advance  of  it.  Thus,  let 
Mercury  come  into  inferior  conjunction  with  the  earth 
at  C,  Fig.  51.  In  about  eighty-eight  days,  the  planet 
will  come  round  to  the  same  point  again  ;  but,  mean- 
while, the  earth  has  moved  forward  through  the  arc 
E  E',  and  will  continue  to  move  while  the  planet  is 
moving  more  rapidly  to  overtake  her ;  the  case  being 
analogous  to  that  of  the  hour  and  minute  hand  of  a 
clock. 

Fig.  51. 


The  synodical  period  of  Mercury  is  one  hundred  and 
sixteen  days,  and  that  of  Venus  five  hundred  and  eigh- 
ty-four days.  The  former  is  increased  twenty-eight 
days,  and  the  latter,  three  hundred  and  sixty  days,  by 
the  motion  of  the  earth  ;  so  that  Venus,  after  being  in 
conjunction  with  the  earth,  goes  more  than  twice  round 
the  sun  before  she  comes  into  conjunction  again.  For, 
since  the  earth  is  likewise  in  motion,  and  moves  more 


MERCURY  AND  VENUS.  233 

than  half  as  fast  as  Venus,  by  the  time  the  latter  has 
gone  round  and  returned  to  the  place  where  the  two 
bodies  were  together,  the  earth  is  more  than  half  way 
round,  and  continues  moving,  so  that  it  will  be  a  long 
time  before  Venus  comes  up  with  it. 

The  motion  of  an  inferior  planet  is  direct  in  pass- 
ing through  its  superior  conjunction,  and  retrograde  in 
passing  through  its  inferior  conjunction.  You  will 
recollect  that  the  motion  of  a  heavenly  body  is  said  to 
be  direct  when  it  is  in  the  order  of  the  signs  from  west 
to  east,  and  retrograde  when  it  is  contrary  to  the  order 
of  the  signs,  or  from  east  to  west.  Now  Venus,  while 
going  from  B  through  D  to  A,  (Fig.  51,)  moves  from 
west  to  east,  and  would  appear  to  traverse  the  celes- 
tial vault  B'  S'  A',  from  right  to  left ;  but  in  passing 
from  A  through  C  to  B,  her  course  would  be  retrograde, 
returning  on  the  same  arc  from  left  to  right.  If  the 
earth  were  at  rest,  therefore,  (and  the  sun,  of  course, 
at  rest,)  the  inferior  planets  would  appear  to  oscillate 
backwards  and  forwards  across  the  sun.  But  it  must 
be  recollected  that  the  earth  is  moving  in  the  same  di- 
rection with  the  planet,  as  respects  the  signs,  but  with 
a  slower  motion.  This  modifies  the  motions  of  the 
planet,  accelerating  it  in  the  superior,  and  retarding 
it  in  the  inferior,  conjunction.  Thus,  in  Fig.  51,  Ve- 
nus, while  moving  through  B  D  A,  would  seem  to 
move  in  the  heavens  from  B'  to  A',  were  the  earth  at 
rest ;  but,  mean-while,  the  earth  changes  its  position 
from  E  to  E',  on  which  account  the  planet  is  not  seen 
at  A',  but  at  A",  being  accelerated  by  the  arc  A'  A",  in 
consequence  of  the  earth's  motion.  On  the  other  hand, 
when  the  planet  is  passing  through  its  inferior  conjunc- 
tion A  C  B,  it  appears  to  move  backwards  in  the  heavens 
from  A'  to  B',  if  the  earth  is  at  rest,  but  from  A'  to  B",  if 
the  earth  has  in  the  mean  time  moved  from  E  to  E', 
being  retarded  by  the  arc  B'  B".  Although  the  motions 
of  the  earth  have  the  effect  to  accelerate  the  planet  in 
the  superior  conjunction,  and  to  retard  it  in  the  infe- 
rior, yet,  on  account  of  the  greater  distance,  the  appa- 


234  LETTERS  ON  ASTRONOMY. 

rent  motion  of  the  planet  is  much  slower  in  the  supe- 
rior than  in  the  inferior  conjunction,  Venus  being  the 
whole  breadth  of  her  orbit,  or  one  hundred  and  thirty- 
six  millions  of  miles  further  from  us  when  at  her  great- 
est, than  when  at  her  least,  distance,  as  is  evident  from 
Fig.  51.  When  passing  from  the  superior  to  the 
inferior  conjunction,  or  from  the  inferior  to  the  supe- 
rior, through  the  greatest  elongations,  the  inferior  plan- 
ets are  stationary.  Thus,  (Fig.  51,)  when  the  plan- 
et is  at  A,  the  earth  being  at  E,  as  the  planet's  motion 
is  directly  towards  the  spectator,  he  would  constantly 
project  it  at  the  same  point  in  the  heavens,  namely,  A'; 
consequently,  it  would  appear  to  stand  still.  Or,  when 
at  its  greatest  elongation  on  the  other  side,  at  B,  as  its 
motion  would  be  directly  from  the  spectator,  it  would 
be  seen  constantly  at  B'.  If  the  earth  were  at  rest,  the 
stationary  points  would  be  at  the  greatest  elongations, 
as  at  A  and  B ;  but  the  earth  itself  is  moving  nearly  at 
right  angles  to  the  planet's  motion,  which  makes  the 
planet  appear  to  move  in  the  opposite  direction.  Its 
direct  motion  will  therefore  continue  longer  on  the  one 
side,  and  its  retrograde  motion  longer  on  the  other  side, 
than  would  be  the  case,  were  it  not  for  the  motion  of 
the  earth.  Mercury,  whose  greatest  angular  distance 
from  the  sun  is  nearly  twenty-nine  degrees,  is  station- 
ary at  an  elongation  of  from  fifteen  to  twenty  degrees ; 
and  Venus,  at  about  twenty-nine  degrees,  although  her 
greatest  elongation  is  about  forty-seven  degrees. 

Mercury  and  Venus  exhibit  to  the  telescope  phases 
similar  to  those  of  the  moon.  When  on  the  side  of  their 
inferior  conjunction,  as  from  B  to  C  through  D,  Fig. 
52,  less  than  half  their  enlightened  disk  is  turned  tow- 
ards us,  and  they  appear  horned,  like  the  moon  in 
her  first  and  last  quarters ;  and  when  on  the  side  of 
the  superior  conjunction,  as  from  C  to  B  through  A, 
more  than  half  the  enlightened  disk  is  turned  towards 
us,  and  they  appear  gibbous.  At  the  moment  of  su- 
perior conjunction,  the  whole  enlightened  orb  of  the 
planet  is  turned  towards  the  earth,  and  the  appearance 


MERCURY  AND  VENUS.  235 

would  be  that  of  the  full  moon ;  but  the  planet  is  too 
near  the  sun  to  be  commonly  visible. 

Fig.  52. 


We  should  at  first  thought  expect,  that  each  of  these 
planets  would  be  largest  and  brightest  near  their  infe- 
rior conjunction,  being  then  so  much  nearer  to  us  than 
at  other  times  ;  but  we  must  recollect  that,  when  in  this 
situation,  only  a  small  part  of  the  enlightened  disk  is 
turned  toward  us.  Still,  the  period  of  greatest  bril- 
liancy cannot  be  when  most  of  the  illuminated  side  is 
turned  towards  us,  for  then,  being  at  the  superior  con- 
junction, its  light  will  be  diminished,  both  by  its  great 
distance,  and  by  its  being  so  near  the  sun  as  to  be 
partially  lost  in  the  twilight.  Hence,  when  Venus  is  a 
little  within  her  place  of  greatest  elongation,  about  for- 
ty degrees  from  the  sun,  although  less  than  half  her  disk 
is  enlightened,  yet,  being  comparatively  near  to  us,  and 
shining  at  a  considerable  altitude  after  the  evening  or 
before  the  morning  twilight,  she  then  appears  in  great- 
est splendor,  and  presents  an  object  admired  for  its 
beauty  in  all  ages.  Thus  Milton, 

*'  Fairest  of  stars,  last  in  the  train  of  night, 
If  better  thou  belong  not  to  the  dawn, 
Sure  pledge  of  day  that  crown'st  the  smiling  morn 
With  thy  bright  circlet." 

Mercury  and  Venus  both  revolve  on  their  axes  in 
nearly  the  same  time  with  the  earth.  The  diurnal  pe- 
riod of  Mercury  is  a  little  greater,  and  that  of  Venus  a 
little  less,  than  twenty-four  hours.  These  revolutions 


236  LETTERS  ON  ASTRONOMY. 

have  been  determined  by  means  of  some  spot  or  mark 
seen  by  the  telescope,  as  the  revolution  of  the  sun  on 
his  axis  is  ascertained  by  means  of  his  spots.  Mercury 
owes  most  of  its  peculiarities  to  its  proximity  to  the  sun. 
Its  light  and  heat,  derived  from  the  sun,  are  estimated 
to  be  nearly  seven  times  as  great  as  on  the  earth,  and 
the  apparent  magnitude  of  the  sun  to  a  spectator  on 
Mercury  would  be  seven  times  greater  than  to  us. 
Hence  the  sun  would  present  to  an  inhabitant  of  that 
planet,  with  eyes  like  ours,  an  object  of  insufferable 
brightness ;  and  all  objects  on  the  surface  would  be 
arrayed  in  a  light  more  glorious  than  we  can  well  imag- 
ine. (See  Fig.  53.)  The  average  heat  on  the  greater 
portion  of  this  planet  would  exceed  that  of  boiling  wa- 
ter, and  therefore  be  incompatible  with  the  existence 
both  of  an  animal  and  a  vegetable  kingdom  constituted 
like  ours. 

The  motion  of  Mercury,  in  his  revolution  round  the 
sun,  is  swifter  than  that  of  any  other  planet,  being  more 
than  one  hundred  thousand  miles  every  hour ;  whereas 
that  of  the  earth  is  less  than  seventy  thousand.  Eigh- 
teen hundred  miles  every  minute, — crossing  the  Atlan- 
tic ocean  in  less  than  two  minutes, — this  is  a  velocity 
of  which  we  can  form  but  a  very  inadequate  conception, 
although,  as  we  shall  see  hereafter,  it  is  far  less  than 
comets  sometimes  exhibit. 

Venus  is  regarded  as  the  most  beautiful  of  the  plan- 
ets, and  is  well  known  as  the  morning  and  evening 
star.  The  most  ancient  nations,  indeed,  did  not  recog- 
nise the  morning  and  evening  star  as  one  and  the  same 
body,  but  supposed  they  were  different  planets,  and 
accordingly  gave  them  different  names,  calling  the 
morning  star  Lucifer,  and  the  evening  star  Hesperus. 
At  her  period  of  greatest  splendor,  Venus  casts  a  shad- 
ow, and  is  sometimes  visible  in  broad  daylight.  Her 
light  is  then  estimated  as  equal  to  that  of  twenty  stars 
of  the  first  magnitude.  In  the  equatorial  regions  of  the 
earth,  where  the  twilight  is  short,  and  Venus,  at  her 
greatest  elongation,  appears  very  high  above  the  hori- 


Fiu.  53. 


rom  the 
Earth. 


From 
Vesta. 


From 
Mars. 


APPARENT  MAGNITUDES  OF  THE  SUN, 

AS  SEEN  FROM  THE  DIFFERENT  PLANETS. 


flrW 


Figures  54,  55,  56. 


VENUS  AND   MARS, 


MERCURY  AND  VENUS.  237 

zon,  her  splendors  are  said  to  be  far  more  conspicuous 
than  in  our  latitude. 

Every  eight  years,  Venus  forms  her  conjunction  with 
the  sun  in  the  same  part  of  the  heavens.  Whatever 
appearances,  therefore,  arise  from  her  position  with  re- 
spect to  the  earth  and  the  sun,  they  are  repeated  every 
eight  years,  in  nearly  the  same  form. 

Thus,  every  eight  years,  Venus  is  remarkably  con- 
spicuous, so  as  to  be  visible  in  the  day-time,  being  then 
most  favorably  situated,  on  several  accounts ;  namely, 
being  nearest  the  earth,  and  at  the  point  in  her  orbit 
where  she  gives  her  greatest  brilliancy,  that  is,  a  little 
within  the  place  of  greatest  elongation.  This  is  the  pe- 
riod for  obtaining  fine  telescopic  views  of  Venus,  when 
she  is  seen  with  spots  on  her  disk.  Thus  two  figures 
of  the  annexed  diagram  (Fig.  54)  represent  Venus  as 
seen  near  her  inferior  conjunction,  and  at  the  period  of 
maximum  brilliancy.  The  former  situation  is  favora- 
ble for  viewing  her  inequalities  of  surface,  as  indicated 
by  the  roughness  of  the  line  which  separates  the  en- 
lightened from  the  unenlightened  part,  (the  termina- 
tor.) According  to  Schroeter,  a  German  astronomer, 
Venus  has  mountains  twenty-two  miles  high.  Her 
mountains,  however,  are  much  more  difficult  to  be  seen 
than  those  of  the  moon. 

The  sun  would  appear,  as  seen  from  Venus,  twice 
as  large  as  on  the  earth,  and  its  light  and  heat  would 
be  augmented  in  the  same  proportion.  (See  Fig.  53.) 
In  many  respects,  however,  the  phenomena  of  this 
planet  are  similar  to  those  of  our  own ;  and  the  gene- 
ral likeness  between  Venus  and  the  earth,  in  regard  to 
dimensions,  revolutions,  and  seasons,  is  greater  than 
exists  between  any  other  two  bodies  of  the  system. 

I  will  only  add  to  the  present  Letter  a  few  words  on 
the  transits  of  the  inferior  planets. 

The  transit  of  Mercury  or  Venus  is  its  passage  across 
the  sun's  disk,  as  the  moon  passes  over  it  in  a  solar 
eclipse.  The  planet  is  seen  projected  on  the  sun's 
disk  in  a  small,  black,  round  spot,  moving  slowly  over 


238  LETTERS  ON  ASTRONOMY. 

the  face  of  the  sun.  As  the  transit  takes  place  only 
when  the  planet  is  in  inferior  conjunction,  at  which 
time  her  motion  is  retrograde,  it  is  always  from  left  to 
right ;  and,  on  account  of  its  motion  being  retarded  by 
the  motion  of  the  earth,  (as  was  explained  by  Fig.  51, 
page  232,)  it  remains  sometimes  a  long  time  on  the  solar 
disk.  Mercury,  when  it  makes  its  transit  across  the  sun's 
centre,  may  remain  on  the  sun  from  five  to  seven  hours. 
You  may  ask,  why  we  do  not  observe  this  appear- 
ance every  time  one  of  the  inferior  planets  comes  into 
inferior  conjunction,  for  then,  of  course,  it  passes  be- 
tween us  and  the  sun.  It  must,  indeed,  at  this  time, 
cross  the  meridian  at  the  same  time  with  the  sun ;  but, 
because  its  orbit  is  inclined  to  that  of  the  sun,  it  may 
cross  it  (and  generally  does)  a  little  above  or  a  little  be- 
low the  sun.  It  is  only  when  the  conjunction  takes 
place  at  or  very  near  the  point  where  the  two  orbits  cross 
one  another,  that  is,  near  the  node,  that  a  transit  can 
occur.  Thus,  if  the  orbit  of  Mercury,  N  M  R,  Fig.  50, 
(page  231,)  were  in  the  same  plane  with  the  earth's  or- 
bit, (and  of  course  with  the  sun's  apparent  orbit,)  then, 
when  the  planet  was  at  Q,,  in  its  inferior  conjunction, 
the  earth  being  at  E,  it  would  always  be  projected  on 
the  sun's  disk  at  Z,  on  the  concave  sphere  of  the  heav- 
ens, and  a  transit  would  happen  at  every  inferior  con- 
junction. But  now  let  us  take  hold  of  the  point  R, 
and  lift  the  circle  which  represents  the  orbit  of  Mercu- 
ry upwards  seven  degrees,  letting  it  turn  upon  the  diam- 
eter d  b  ;  then,  we  may  easily  see  that  a  spectator  at  E 
would  project  the  planet  higher  in  the  heavens  than 
the  sun ;  and  such  would  always  be  the  case,  except 
when  the  conjunction  takes  place  at  the  node.  Then 
the  point  of  intersection  of  the  two  orbits  being  in  one 
and  the  same  plane,  both  bodies  would  be  referred  to 
the  same  point  on  the  celestial  sphere.  As  the  sun, 
in  his  apparent  revolution  around  the  earth  every  year, 
passes  through  every  point  in  the  ecliptic,  of  course 
he  must  every  year  be  at  each  of  the  points  where  the 
orbit  of  Mercury  or  Venus  crosses  the  ecliptic,  that  is, 


MERCURY  AND  VENUS.  239 

at  eacl>  of  the  nodes  of  one  of  these  planets  ;*  and  as 
these  nodes  are  on  opposite  sides  of  the  ecliptic,  con- 
sequently, the  sun  will  pass  through  them  at  opposite 
seasons  of  the  year,  as  in  January  and  July,  February 
and  August.  Now,  should  Mercury  or  Venus  happen 
to  come  between  us  and  the  sun,  just  as  the  sun  is  pass- 
ing one  of  the  planet's  nodes,  a  transit  would  happen. 
Hence  the  transits  of  Mercury  take  place  in  May  and 
November,  and  those  of  Venus,  in  June  and  December. 

Transits  of  Mercury  occur  more  frequently  than 
those  of  Venus.  The  periodic  times  of  Mercury  and 
the  earth  are  so  adjusted  to  each  other,  that  Mercury 
performs  nearly  twenty-nine  revolutions  while  the  earth 
performs  seven.  If,  therefore,  the  two  bodies  meet  at 
the  node  in  any  given  year,  seven  years  afterwards  they 
will  meet  nearly  at  the  same  node,  and  a  transit  may 
take  place,  accordingly,  at  intervals  of  seven  years. 
But  fifty-four  revolutions  of  Mercury  correspond  still 
nearer  to  thirteen  revolutions  of  the  earth ;  and  there- 
fore a  transit  is  still  more  probable  after  intervals  of  thir- 
teen years.  At  intervals  of  thirty-three  years,  transits 
of  Mercury  are  exceedingly  probable,  because  in  that 
time  Mercury  makes  almost  exactly  one  hundred  and 
thirty-seven  revolutions.  Intermediate  transits,  howev- 
er, may  occur  at  the  other  node.  Thus,  transits  of 
"Mercury  happened  at  the  ascending  node  in  1815,  and 
1822,  at  intervals  of  seven  years ;  and  at  the  descend- 
ing node  in  1832,  which  will  return  in  1845,  after  thir- 
teen years. 

Transits  of  Venus  are  events  of  very  unfrequent  oc- 
currence. Eight  revolutions  of  the  earth  are  com- 
pleted in  nearly  the  same  time  as  thirteen  revolutions 
of  Venus  ;  and  hence  two  transits  of  Venus  may  oc- 
cur after  an  interval  of  eight  years,  as  was  the  case  at 
the  last  return  of  the  phenomenon,  one  transit  having 
occurred  in  1761,  and  another  in  1769.  But  if  a  tran- 

*  You  will  recollect  that  the  sun  is  said  to  be  at  the  node,  when 
the  places  of  the  node  and  the  sun  are  both  projected,  by  a  spectator 
on  the  earth,  upon  the  same  part  of  the  heavens. 


240  LETTERS  ON  ASTRONOMY. 

sit  does  not  happen  after  eight  years,  it  will  not  happen 
at  the  same  node,  until  an  interval  of  two  hundred  and 
thirty-five  years  :  but  intermediate  transits  may  occur  a; 
the  other  node.  The  next  transit  of  Venus  will  tak 
place  in  1874,  being  two  hundred  and  thirty-five  year 
after  the  first  that  was  ever  observed,  which  occurred 
in  1639.  This  was  seen,  for  the  first  time  by  morta 
eyes,  by  two  youthful  English  astronomers,  Horrox 
and  Crabtree.  Horrox  was  a  young  man  of  extraor- 
dinary promise,  and  indicated  early  talents  for  prac- 
tical astronomy,  which  augured  the  highest  eminence  ; 
but  he  died  in  the  twenty-third  year  of  his  age.  He 
was  only  twenty  when  the  transit  appeared,  and  he  had 
made  the  calculations  and  observations,  by  which  he 
was  enabled  to  anticipate  its  arrival  several  years  before. 
At  the  approach  of  the  desired  time  for  observing  the 
transit,  he  received  the  sun's  image  through  a  telescope 
in  a  dark  room  upon  a  white  piece  of  paper,  and  after 
waiting  many  hours  with  great  impatience,  (as  his  cal- 
culation did  not  lead  him  to  a  knowledge  of  the  precise 
time  of  the  occurrence,)  at  last,  on  the  twenty-fourth  of 
November,  1639,  old  style,  at  three  and  a  quarter 
hours  past  twelve,  just  as  he  returned  from  church,  he 
had  the  pleasure  to  find  a  large  round  spot  near  the  limb 
of  the  sun's  image.  It  moved  slowly  across  the  sun's 
disk,  but  had  not  entirely  left  it  when  the  sun  set. 

The  great  interest  attached  by  astronomers  to  a 
transit  of  Venus  arises  from  its  furnishing  the  most  ac- 
curate means  in  our  power  of  determining  the  surfs 
horizontal  parallax, — an  element  of  great  importance, 
since  it  leads  us  to  a  knowledge  of  the  distance  of  the 
earth  from  the  sun,  which  again  affords  the  means  of 
estimating  the  distances  of  all  the  other  planets,  and 
possibly,  of  the  fixed  stars.  Hence,  in  1769,  great  ef- 
forts were  made  throughout  the  civilized  world,  under 
the  patronage  of  different  governments,  to  observe  this 
phenomenon  under  circumstances  the  most  favorable 
for  determining  the  parallax  of  the  sun. 

The  common  methods  of  finding  the  parallax  of  a 


MERCURY  AND  VENUS.  241 

heavenly  body  cannot  be  relied  on  to  a  greater  degree 
of  accuracy  than  four  seconds.  In  the  case  of  the 
moon,  whose  greatest  parallax  amounts  to  about  one 
legree,  this  deviation  from  absolute  accuracy  is  not 
very  material ;  but  it  amounts  to  nearly  half  the  entire 
parallax  of  the  sun. 

If  the  sun  and  Venus  were  equally  distant  from  us, 
they  would  be  equally  affected  by  parallax,  as  viewed 
by  spectators  in  different  parts  of  the  earth,  and  hence 
their  relative  situation  would  not  be  altered  by  it ;  but 
since  Venus,  at  the  inferior  conjunction,  is  only  about 
one  third  as  far  off  as  the  sun,  her  parallax  is  pro- 
portionally greater,  and  therefore  spectators  at  distant 
points  will  see  Venus  projected  on  different  parts  of  the 
solar  disk,  as  the  planet  traverses  the  disk.  Astrono- 
mers avail  themselves  of  this  circumstance  to  ascertain 
the  sun's  horizontal  parallax,  which  they  are  enabled  to 
do  by  comparing  it  with  that  of  Venus,  in  a  manner 
which,  without  a  knowledge  of  trignometry,  you  will 
not  fully  understand.  In  order  to  make  the  difference 
in  the  apparent  places  of  Venus  on  the  sun's  disk  as 
great  as  possible,  very  distant  places  are  selected  for 
observation.  Thus,  in  the  transits  of  1761  and  1769, 
several  of  the  European  governments  fitted  out  expen- 
sive expeditions  to  parts  of  the  earth  remote  from  each 
other.  For  this  purpose,  the  celebrated  Captain  Cook, 
in  1769,  went  to  the  South  Pacific  Ocean,  and  observ- 
ed the  transit  at  the  island  of  Otaheite,  while  others 
went  to  Lapland,  for  the  same  purpose,  and  others  still, 
to  many  other  parts  of  the  globe.  Thus,  suppose  two 
observers  took  their  stations  on  opposite  sides  of  the 
earth,  as  at  A,  and  B,  Fig.  57,  page  242;  at  A,  the 
planet  V  would  be  seen  on  the  sun's  disk  at  a,  while 
at  B,  it  would  be  seen  at  b. 

The  appearance  of  Venus  on  the  sun's  disk  being 
that  of  a  well-defined  black  spot,  and  the  exactness 
with  which  the  moment  of  external  or  internal  contact 
may  be  determined,  are  circumstances  favorable  to  the 
exactness  of  the  result ;  and  astronomers  repose  so- 

21  L.  A. 


242 


LETTERS  ON  ASTRONOMY. 


Fig.  57.  much  confidence  in  the  estimation  of 
the  sun's  horizontal  parallax,  as  de- 
rived from  observations  on  the  transit 
of  1769,  that  this  important  element  is 
thought  to  be  ascertained  within  one 
tenth  of  a  second.  The  general  re- 
sult of  all  these  observations  gives  the 
sun's  horizontal  parallax  eight  seconds 
and  six  tenths, — a  result  which  shows 
at  once  that  the  sun  must  be  a  great 
way  off,  since  the  semidiameter  of  the 
earth,  a  line  nearly  four  thousand  miles 
in  length,  would  appear  at  the  sun  un- 
der an  angle  less  than  one  four  hun- 
dredth of  a  degree.  During  the  tran- 
sits of  Venus  over  the  sun's  disk,  in 
1761  and  1769,  a  sort  of  penumbral 
light  was  observed  around  the  plan- 
et, by  several  astronomers,  which  was 
thought  to  indicate  an  atmosphere. 
This  appearance  was  particularly  ob- 
servable while  the  planet  was  coming 
on  or  going  off  the  solar  disk.  The 
total  immersion  and  emersion  were  not 
instantaneous ;  but  as  two  drops  of 
water,  when  about  to  separate,  form  a 
ligament  between  them,  so  there  was 
a  dark  shade  stretched  out  between  Venus  and  the 
sun ;  and  when  the  ligament  broke,  the  planet  seemed 
to  have  got  about  an  eighth  part  of  her  diameter  from 
the  limb  of  the  sun.  The  various  accounts  of  the  two 
transits  abound  with  remarks  like  these,  which  indicate 
the  existence  of  an  atmosphere  about  Venus  of  near- 
ly the  density  and  extent  of  the  earth's  atmosphere. 
Similar  proofs  of  the  existence  of  an  atmosphere  around 
this  planet  are  derived  from  appearances  of  twilight. 

The  elder  astronomers  imagined  that  they  had  dis- 
covered a  satellite  accompanying  Venus  in  her  transit. 
If  Venus  had  in  reality  any  satellite,  the  fact  would 


SUPERIOR  PLANETS.  243 

be  obvious  at  her  transits,  as,  in  some  of  them  at  least, 
it  is  probable  that  the  satellite  would  be  projected  near 
the  primary  on  the  sun's  disk ;  but  later  astronomers 
have  searched  in  vain  for  any  appearances  of  the  kind, 
and  the  inference  is,  that  former  astronomers  were  de- 
ceived by  some  optical  illusion. 


LETTER  XXI. 

SUPERIOR  PLANETS  !    MARS,  JUPITER,   SATURN,  AND  URANUS. 

"  With  what  an  awful,  world-revolving  power, 
Were  first  the  unwieldy  planets  launched  along 
The  illimitable  void  !    There  to  remain 
Amidst  the  flux  of  many  thousand  years, 
That  oft  has  swept  the  toiling  race  of  men, 
And  all  their  labored  monuments,  away."— Thomson. 

MERCURY  AND  VENUS,  as  we  have  seen,  are  always 
observed  near  the  sun,  and  from  this  circumstance,  as 
well  as  from  the  changes  of  magnitude  and  form  which 
they  undergo,  we  know  that  they  have  their  orbits 
within  that  of  the  earth,  and  hence  we  call  them  infe- 
rior planets.  On  the  other  hand,  Mars,  Jupiter,  Sa- 
turn, and  Uranus,  exhibit  such  appearances,  at  different 
times,  as  show  that  they  revolve  around  the  sun  at  a 
greater  distance  than  the  earth,  and  hence  we  denomi- 
nate them  superior  planets.  We  know  that  they  nev- 
er come  between  us  and  the  sun,  because  they  never 
undergo  those  changes  which  Mercury  and  Venus,  as 
well  as  the  moon,  sustain,  in  consequence  of  their  com- 
ing into  such  a  position.  They,  however,  wander  to 
the  greatest  angular  distance  from  the  sun,  being  some- 
times seen  one  hundred  and  eighty  degrees  from  him, 
so  as  to  rise  when  the  sun  sets.  All  these  different, 
appearances  must  naturally  result  from  their  orbits'  be- 
ing exterior  to  that  of  the  earth,  as  will  be  evident  from 
the  following  representation.  Let  E,  Fig.  58,  page  244, 
be  the  earth,  and  M,  one  of  the  superior  planets,  Mars, 
for  example,  each  body  being  seen  in  its  path  around  the 


244 


LETTERS  ON  ASTRONOMY. 
Fig.  58. 


sun.  At  M,  the  planet  would  be  in  opposition  to  the 
sun,  like  the  moon  at  the  full ;  at  Q,,  and  Q,',  it  would  be 
seen  ninety  degrees  off,  or  in  quadrature  ;  and  at  M',  in 
conjunction.  We  know,  however,  that  this  must  be  a 
superior  and  not  an  inferior  conjunction,  for  the  illumi- 
nated disk  is  still  turned  towards  us  ;  whereas,  if  it  came 
between  us  and  the  sun,  like  Mercury,  or  Venus,  in  its 
inferior  conjunction,  its  dark  side  would  be  presented 
to  us. 

The  superior  planets  do  not  exhibit  to  the  telescope 
different  phases,  but,  with  a  single  exception,  they  al- 
ways present  the  side  that  is  turned  towards  the  earth 
fully  enlightened.  This  is  owing  to  their  great  dis- 
tance from  the  earth ;  for  were  the  spectator  to  stand 
upon  the  sun,  he  would  of  course  always  have  the  illu- 
minated side  of  each  of  the  planets  turned  towards 
him ;  but  so  distant  are  all  the  superior  planets,  except 
Mars,  that  they  are  viewed  by  us  very  nearly  in  the 
same  manner  as  they  would  be  if  we  actually  stood  on 
the  sun.  Mars,  however,  is  sufficiently  near  to  appear 
somewhat  gibbous  when  at  or  near  one  of  its  quadra- 
tures. Thus,  when  the  planet  is  at  Q,  it  is  plain  that, 


SUPERIOR  PLANETS.  245 

of  the  hemisphere  that  is  turned  towards  the  earth,  a 
small  part  is  unilluminated. 

MARS  is  a  small  planet,  his  diameter  being  only  about 
half  that  of  the  earth,  or  four  thousand  two  hundred 
miles.  He  also,  at  times,  comes  nearer  to  the  earth 
than  any  other  planet,  except  Venus.  His  mean  dis- 
tance from  the  sun  is  one  hundred  and  forty-two  mil- 
lions of  miles  ;  but  his  orbit  is  so  elliptical,  that  his  dis- 
tance varies  much  in  different  parjts  of  his  revolution. 
Mars  is  always  very  near  the  ecliptic,  never  varying 
from  it  more  than  two  degrees.  He  is  distinguished 
from  all  the  planets  by  his  deep  red  color,  and  fiery  as- 
pect ;  but  his  brightness  and  apparent  magnitude  vary 
much,  at  different  times,  being  sometimes  nearer  to  us 
than  at  others  by  the  whole  diameter  of  the  earth's  or- 
bit ;  that  is,  by  about  one  hundred  and  ninety  millions 
of  miles.  When  Mars  is  on  the  same  side  of  the  sun 
with  the  earth,  or  at  his  opposition,  he  comes  within 
forty-seven  millions  of  miles  of  the  earth,  and,  rising 
about  the  time  the  sun  sets,  surprises  us  by  his  magni- 
tude and  splendor ;  but  when  he  passes  to  the  other 
side  of  the  sun,  to  his  superior  conjunction,  he  dwindles 
to  the  appearance  of  a  small  star,  being  then  two  hun- 
dred and  thirty-seven  millions  of  miles  from  us.  Thus, 
let  M,  Fig,  58,  represent  Mars  in  opposition,  and  M',  in 
the  superior  conjunction,  while  E  represents  the  earth. 
It  is  obvious  that,  in  the  former  situation,  the  planet 
must  be  nearer  to  the  earth  than  in  the  latter,  by  the 
whole  diameter  of  the  earth's  orbit.  When  viewed  with 
a  powerful  telescope,  the  surface  of  Mars  appears  di- 
versified with  numerous  varieties  of  light  and  shade. 
The  region  around  the  poles  is  marked  by  white  spots, 
(see  Fig.  56,  page  237,)  which  vary  their  appearances 
with  the  changes  of  seasons  in  the  planet.  Hence  Dr. 
Herschel  conjectured  that  they  were  owing  to  ice  and 
snow,  which  alternately  accumulate  and  melt  away, 
according  as  it  is  Winter  or  Summer,  in  that  region. 
They  are  greatest  and  most  conspicuous  when  that  part 
of  the  planet  has  just  emerged  from  a  long- Winter,  and 
21* 


246  LETTERS  ON  ASTRONOMY. 

they  gradually  waste  away,  as  they  are  exposed  to  the 
solar  heat.  Fig.  56,  represents  the  planet,  as  exhibited, 
under  the  most  favorable  circumstances,  to  a  powerful 
telescope,  at  the  time  when  its  gibbous  form  is  striking- 
ly obvious.  It  has  been  common  to  ascribe  the  ruddy 
light  of  Mars  to  an  extensive  and  dense  atmosphere, 
which  was  said  to  be  distinctly  indicated  by  the  gradual 
diminution  of  light  observed  in  a  star,  as  it  approaches 
very  near  to  the  planet,  in  undergoing  an  occultation  ; 
but  more  recent  observations  afford  no  such  evidence 
of  an  atmosphere. 

By  observations  on  the  spots,  we  learn  that  Mars  re- 
volves on  his  axis  in  very  nearly  the  same  time  with  the 
earth,  (twenty-four  hours  thirty-nine  minutes  twenty-one 
seconds  and  three  tenths,)  and  that  the  inclination  of 
his  axis  to  that  of  his  orbit  is  also  nearly  the  same,  be- 
ing thirty  degrees  eighteen  minutes  ten  seconds  and 
eight  tenths.  Hence  the  changes  of  day  and  night 
must  be  nearly  the  same  there  as  here,  and  the  seasons 
also  very  similar  to  ours.  Since,  however,  the  distance 
of  Mars  from  the  sun  is  one  hundred  and  forty-two 
while  that  of  the  earth  is  only  ninety-five  millions  of 
miles,  the  sun  will  appear  more  than  twice  as  small  on 
that  planet  as  on  ours,  (see  Fig.  53,  page  236,)  and  its 
light  and  heat  will  be  diminished  in  the  same  propor- 
tion. Only  the  equatorial  regions,  therefore,  will  be 
suitable  for  the  existence  of  animals  and  vegetables. 

The  earth  will  be  seen  from  Mars  as  an  inferior  plan- 
et, always  near  the  sun,  presenting  appearances  similar, 
in  many  respects,  to  those  which  Venus  presents  to  us. 
It  will  be  to  that  planet  the  evening  and  morning  star, 
sung  by  their  poets  (if  poets  they  have)  with  a  like  en- 
thusiasm. The  moon  will  attend  the  earth  as  a  little 
star,  being  never  seen  further  from  her  side  than  about 
the  diameter  under  which  we  view  the  moon.  To  the 
telescope,  the  earth  will  exhibit  phases  similar  to  those 
of  Venus  ;  and,  finally,  she  will,  at  long  intervals,  make 
her  transits  over  the  solar  disk.  Mean-while,  Venus  will 
stand  to  Mars  in  a  relation  similar  to  that  of  Mercury 


SUPERIOR  PLANETS.  247 

to  us,  revealing  herself  only  when  at  the  periods  of  her 
greatest  elongation,  and  at  all  other  times  hiding  her- 
self within  the  solar  blaze.  Mercury  will  never  be  vis- 
ible to  an  inhabitant  of  Mars. 

JUPITER  is  distinguished  from  all  the  other  planets 
by  his  great  magnitude.  His  diameter  is  eighty-nine 
thousand  miles,  and  his  volume  one  thousand  two  hun- 
dred and  eighty  times  that  of  the  earth,  s  His  figure  is 
strikingly  spheroidal,  the  equatorial  being  more  than 
six  thousand  miles  longer  than  the  polar  diameter. 
Such  a  figure  might  naturally  be  expected  from  the 
rapidity  of  his  diurnal  rotation,  which  is  accomplished 
in  about  ten  hours.  A  place  on  the  equator  of  Jupiter 
must  turn  twenty-seven  times  as  fast  as  on  the  terres- 
trial equator.  The  distance  of  Jupiter  from  the  sun  is 
nearly  four  hundred  and  ninety  millions  of  miles,  and 
his  revolution  around  the  sun  occupies  nearly  twelve 
years.  Every  thing  appertaining  to  Jupiter  is  on  a  grand 
scale.  A  world  in  itself,  equal  in  dimensions  to  twelve 
hundred  and  eighty  of  ours  ;  the  whole  firmament  roll- 
ing round  it  in  the  short  space  of  ten  hours,  a  move- 
ment so  rapid  that  the  eye  could  probably  perceive  the 
heavenly  bodies  to  change  their  places  every  moment ; 
its  year  dragging  out  a  length  of  more  than  four  thous- 
and days,  and  more  than  ten  thousand  of  its  own  days, 
while  its  nocturnal  skies  are  lighted  up  with  four  bril- 
liant moons  ; — these  are  some  of  the  peculiarities  which 
characterize  this  magnificent  planet. 

The  view  of  Jupiter  through  a  good  telescope  is  one 
of  the  most  splendid  and  interesting  spectacles  in  astron- 
omy. The  disk  expands  into  a  large  and  bright  orb, 
like  the  full  moon ;  the  spheroidal  figure  which  theory 
assigns  to  revolving  spheres,  especially  to  those  which 
turn  with  great  velocity,  is  here  palpably  exhibited  to 
the  eye ;  across  the  disk,  arranged  in  parallel  stripes, 
are  discerned  several  dusky  bands,  called  belts ;  and 
four  bright  satellites,  always  in  attendance,  and  ever  va- 
rying their  positions,  compose  a  splendid  retinue.  In- 
deed, astronomers  gaze  with  peculiar  interest  on  Jupiter 


248  LETTERS  ON  ASTRONOMY. 

and  his  moons,  as  affording  a  miniature  representation 
of  the  whole  solar  system,  repeating,  on  a  smaller  scale, 
the  same  revolutions,  and  exemplifying  more  within  the 
compass  of  our  observation,  the  same  laws  as  regulate 
the  entire  assemblage  of  sun  and  planets.  Figure  59, 
facing  page  247,  gives  a  correct  view  of  Jupiter,  as  ex- 
hibited to  a  powerful  telescope  in  a  clear  evening.  You 
will  remark  his  flattened  or  spheroidal  figure,  the  belts 
which  appear  in  parallel  stripes  across  his  disk,  and  the 
four  satellites,  that  are  seen  like  little  stars  in  a  straight 
line  with  the  equator  of  the  planet. 

The  belts  of  Jupiter  are  variable  in  their  number 
and  dimensions.  With  the  smaller  telescopes  only  one 
or  two  are  seen,  and  those  across  the  equatorial  regions  ; 
but  with  more  powerful  instruments,  the  number  is  in- 
creased, covering  a  large  part  of  the  entire  disk.  Dif- 
ferent opinions  have  been  entertained  by  astronomers 
respecting  the  cause  of  these  belts  ;  but  they  have  gen- 
erally been  regarded  as  clouds  formed  in  the  atmos- 
phere of  the  planet,  agitated  by  winds,  as  is  indicated 
by  their  frequent  changes,  and  made  to  assume  the 
form  of  belts  parallel  to  the  equator,  like  currents  that 
circulate  around  our  globe.  Sir  John  Herschel  sup- 
poses that  the  belts  are  not  ranges  of  clouds,  but  por- 
tions of  the  planet  itself,  brought  into  view  by  the  re- 
moval of  clouds  and  mists,  that  exist  in  the  atmosphere 
of  the  planet,  through  which  are  openings  made  by 
currents  circulating  around  Jupiter. 

The  satellites  of  Jupiter  may  be  seen  with  a  tele- 
scope of  very  moderate  powers.  Even  a  common  spy- 
glass will  enable  us  to  discern  them.  Indeed,  one  or 
two  of  them  have  been  occasionally  seen  with  the  na- 
ked eye.  In  the  largest  telescopes  they  severally  ap- 
pear as  bright  as  Sirius.  With  such  an  instrument, 
the  view  of  Jupiter,  with  his  moons  and  belts,  is  truly 
a  magnificent  spectacle.  As  the  orbits  of  the  satellites 
do  not  deviate  far  from  the  plane  of  the  ecliptic,  and 
but  little  from  the  equator  of  the  planet,  they  are  us- 
ually seen  in  nearly  a  straight  line  with  each  other,  ex- 


SUPERIOR  PLANETS.  249 

tending  across  the  central  part  of  the  disk.  (See  Fig. 
59,  facing  page  247.) 

Jupiter  and  his  satellites  exhibit  in  miniature  all  the 
phenomena  of  the  solar  system.  The  satellites  per- 
form, around  their  primary,  revolutions  very  analogous 
to  those  which  the  planets  perform  around  the  sun, 
having,  in  like  manner,  motions  alternately  direct,  sta- 
tionary, and  retrograde.  They  are  all,  with  one  excep- 
tion, a  little  larger  than  the  moon ;  and  the  second  sat- 
ellite, which  is  the  smallest,  is  nearly  as  large  as  the 
moon,  being  two  thousand  and  sixty-eight  miles  in  di- 
ameter. They  are  all  very  small  compared  with  the 
primary,  the  largest  being  only  one  twenty-sixth  part 
of  the  primary.  The  outermost  satellite  extends  to 
the  distance  from  the  planet  of  fourteen  times  his  di- 
ameter. The  whole  system,  therefore,  occupies  a  re- 
gion of  space  more  than  one  million  miles  in  breadth. 
Rapidity  of  motion,  as  well  as  greatness  of  dimensions, 
is  characteristic  of  the  system  of  Jupiter.  I  have  al- 
ready mentioned  that  the  planet  itself  has  a  motion  on 
its  own  axis  much  swifter  than  that  of  the  earth,  and 
the  motions  of  the  satellites  are  also  much  more  rapid 
than  that  of  the  moon.  The  innermost,  which  is  a 
little  further  off  than  the  moon  is  from  the  earth,  goes 
round  its  primary  in  about  a  day  and  three  quarters ; 
and  the  outermost  occupies  less  than  seventeen  days. 

The  orbits  of  the  satellites  are  nearly  or  quite  circu- 
lar, and  deviate  but  little  from  the  plane  of  the  plari- 
et's  equator,  and  of  course  are  but  slightly  inclined  to 
the  plane  of  his  orbit.  They  are  therefore  in  a  similar 
situation  with  respect  to  Jupiter,  as  the  moon  would  be 
with  respect  to  the  earth,  if  her  orbit  nearly  coincided 
with  the  ecliptic,  in  which  case,  she  would  undergo  an 
eclipse  at  every  opposition.  The  eclipses  of  Jupiter's 
satellites,  in  their  general  circumstances,  are  perfectly 
analogous  to  those  of  the  moon,  but  in  their  details 
they  differ  in  several  particulars.  Owing  to  the  much 
greater  distance  of  Jupiter  from  the  sun,  and  its  great- 
er magnitude,  the  cone  of  its  shadow  is  much  longer 


250  LETTERS  ON  ASTRONOMY. 

and  larger  than  that  of  the  earth.  On  this  account, 
as  well  as  on  account  of  the  little  inclination  of  their 
orbit  to  that  of  the  primary,  the  three  inner  satellites 
of  Jupiter  pass  through  his  shadow,  and  are  totally 
eclipsed,  at  every  revolution.  The  fourth  satellite,  ow- 
ing to  the  greater  inclination  of  its  orbit,  sometimes, 
though  rarely,  escapes  eclipse,  and  sometimes  merely 
grazes  the  limits  of  the  shadow,  or  suffers  a  partial 
eclipse.  These  eclipses,  moreover,  are  not  seen,  as  is 
the  case  with  those  of  the  moon,  from  the  centre  of 
their  motion,  but  from  a  remote  station,  and  one  whose 
situation  with  respect  to  the  line  of  the  shadow  is  vari- 
able. This  makes  no  difference  in  the  times  of  the 
eclipses,  but  it  makes  a  very  great  one  in  their  visibili- 
ty, and  in  their  apparent  situations  with  respect  to  the 
planet  at  the  moment  of  their  entering  or  quitting  the 
shadow. 

The  eclipses  of  Jupiter's  satellites  present  some  cu- 
rious phenomena,  which  you  will  easily  understand  by 
studying  the  following  diagram.     Let  A,  B,  C,  D,  Fig. 
61,  represent  the  earth  in  different  parts  of  its  orbit; 
Fig.  61. 


J,  Jupiter,  in  his  orbit,  surrounded  by  his  four  satellites, 
the  orbits  of  which  are  marked  1,  2,  3,  4.  At  a,  the 
first  satellite  enters  the  shadow  of  the  planet,  emerges 
from  it  at  b,  and  advances  to  its  greatest  elongation  at 
c.  The  other  satellites  traverse  the  shadow  in  a  similar 
manner.  The  apparent  place,  with  respect  to  the  plan 


SUPERIOR  PLANETS. 

marked  by  Roemer,  a  Danish  astronomer,  on  compar- 
ing together  observations  of  these  eclipses  during  many 
successive  years,  that  they  take  place  sooner  by  about 
sixteen  minutes,  when  the  earth  is  on  the  same  side  of 
the  sun  with  the  planet,  than  when  she  is  on  the  oppo- 
site side.  The  difference  he  ascribes  to  the  progres- 
sive motion  of  light,  which  takes  that  time  to  pass 
through  the  diameter  of  the  earth's  orbit,  making  the 
velocity  of  light  about  one  hundred  and  ninety-two 
thousand  miles  per  second.  So  great  a  velocity  start- 
led astronomers  at  first,  and  produced  some  degree  of 
distrust  of  this  explanation  of  the  phenomenon  ;  but 
the  subsequent  discovery  of  what  is  called  the  aber- 
ration of  light,  led  to  an  independent  estimation  of  the 
velocity  of  light,  with  almost  precisely  the  same  result. 

Few  greater  feats  have  ever  been  performed  by  the 
human  mind,  than  to  measure  the  speed  of  light, — a 
speed  so  great,  as  would  carry  it  across  the  Atlantic 
Ocean  in  the  sixty-fourth  part  of  a  second,  and  around 
the  globe  in  less  than  the  seventh  part  of  a  second ! 
Thus  has  man  applied  his  scale  to  the  motions  of  an 
element,  that  literally  leaps  from  world  to  world  in  the 
twinkling  of  an  eye.  This  is  one  example  of  the  great 
power  which  the  invention  of  the  telescope  conferred 
on  man. 

Could  we  plant  ourselves  on  the  surface  of  this  vast 
planet,  we  should  see  the  same  starry  firmament  ex- 
panding over  our  heads  as  we  see  now ;  and  the  same 
would  be  true  if  we  could  fly  from  one  planetary  world 
to  another,  until  we  "made  the  circuit  of  them  all;  but 
the  sun  and  the  planetary  system  would  present  them- 
selves to  us  under  new  and  strange  aspects.  The  sun 
himself  would  dwindle  to  one  twenty-seventh  of  his  pres- 
ent surface,  (Fig.  53,  facing  page  236,)  and  afford  a  de- 
gree of  light  and  heat  proportionally  diminished  ;  Mercu- 
ry, Venus,  and  even  the  Earth,  would  all  disappear,  being 
too  near  the  sun  to  be  visible  ;  Mars  would  be  as  seldom 
seen  as  Mercury  is  by  us,  and  constitute  the  only  inferi- 
or planet.  On  the  other  hand,  Saturn  would  shine  with 

22  L.  A. 


254  LETTERS  ON  ASTRONOMY. 

greatly  augmented  size  and  splendor.  When  in  oppo- 
sition to  the  sun,  (at  which  time  it  comes  nearest  to  Ju- 
piter,) it  would  be  a  grand  object,  appearing  larger  than 
either  Venus  or  Jupiter  does  to  us.  When,  however, 
passing  to  the  other  side  of  the  sun,  through  its  supe- 
rior conjunction,  it  would  gradually  diminish  in  size  and 
brightness,  and  at  length  become  much  less  than  it  ever 
appears  to  us,  since  it  would  then  be  four  hundred  mil- 
lions of  miles  further  from  Jupiter  than  it  ever  is  from  us. 
Although  Jupiter  comes  four  hundred  millions  of 
miles  nearer  to  Uranus  than  the  earth  does,  yet  it  is 
still  thirteen  hundred  millions  of  miles  distant  from  that 
planet.  Hence  the  augmentation  of  the  magnitude  and 
light  of  Uranus  would  be  barely  sufficient  to  render  it 
distinguishable  by  the  naked  eye.  It  appears,  there- 
fore, that  Saturn  is  the  peculiar  ornament  of  the  firma- 
ment of  Jupiter,  and  would  present  to  the  telescope  most 
interesting  and  sublime  phenomena.  As  we  owe  the 
revelation  of  the  system  of  Jupiter  and  his  attendant 
worlds  wholly  to  the  telescope,  and  as  the  discovery 
and  observation  of  them  constituted  a  large  portion  of 
the  glory  of  Galileo,  I  am  now  forcibly  reminded  of  his 
labors,  and  will  recur  to  his  history,  and  finish  the  sketch 
which  I  commenced  in  a  previous  Letter. 


LETTER  XXII. 


COPERNICUS. GALILEO. 

**  They  leave  at  length  the  nether  gloom,  and  stand 
Before  the  portals  of  a  better  land  ; 
To  happier  plains  they  come,  and  fairer  groves, 
The  seats  of  those  whom  Heaven,  benignant,  loves; 
A  brighter  day,  a  bluer  ether,  spreads 
Its  lucid  depths  above  their  favored  heads  ; 
And,  purged  from  mists  that  veil  our  earthly  skies, 
Shine  suns  and  stars  unseen  by  mortal  eyes." — Virgil. 

IN  order  to  appreciate  the  value  of  the  contributions 
which  Galileo  made  to  astronomy,  soon  after  the  inven- 
tion of  the  telescope,  it  is  necessary  to  glance  at  the 
state  of  the  science  when  he  commenced  his  discoveries. 


COPERNICUS.  255 

For  many  centuries,  during  the  middle  ages,  a  dark 
night  had  hung  over  astronomy,  through  which  hardly  a 
ray  of  light  penetrated,  when,  in  the  eastern  part  of  civil- 
ized Europe,  a  luminary  appeared,  that  proved  the  har- 
binger of  a  bright  and  glorious  day.  This  was  Coperni- 
cus, a  native  of  Thorn,  in  Prussia.  He  was  born  in  1473. 
Though  destined  for  the  profession  of  medicine,  from 
his  earliest  years  he  displayed  a  great  fondness  and  ge- 
nius for  mathematical  studies,  and  pursued  them  with 
distinguished  success  in  the  University  of  Cracow.  At 
the  age  of  twenty-five  years,  he  resorted  to  Italy,  for 
the  purpose  of  studying  astronomy,  where  he  resided  a 
number  of  years.  Thus  prepared,  he  returned  to  his 
native  country,  and,  having  acquired  an  ecclesiastical 
living  that  was  adequate  to  his  support  in  his  frugal 
mode  of  life,  he  established  himself  at  Frauenberg,  a 
small  town  near  the  mouth  of  the  Vistula,  where  he 
spent  nearly  forty  years  in  observing  the  heavens,  and 
meditating  on  the  celestial  motions.  He  occupied  the 
upper  part  of  a  humble  farm-house,  through  the  roof  of 
which  he  could  find  access  to  an  unobstructed  sky,  and 
there  he  carried  on  his  observations.  His  instruments, 
however,  were  few  and  imperfect,  and  it  does  not  ap- 
pear that  he  added  any  thing  to  the  art  of  practical  as- 
tronomy. This  was  reserved  for  Tycho  Brahe,  who 
came  a  half  a  century  after  him.  Nor  did  Copernicus 
enrich  the  science  with  any  important  discoveries.  It 
was  not  so  much  his  genius  or  taste  to  search  for  new 
bodies,  or  new  phenomena  among  the  stars,  as  it  was 
to  explain  the  reasons  of  the  most  obvious  and  well- 
known  appearances  and  motions  of  the  heavenly  bo- 
dies. With  this  view,  he  gave  his  mind  to  long-con- 
tinued and  profound  meditation. 

Copernicus  tells  us  that  he  was  first  led  to  think  that 
the  apparent  motions  of  the  heavenly  bodies,  in  their 
diurnal  revolution,  were  owing  to  the  real  motion  of  the 
earth  in  the  opposite  direction,  from  observing  instances 
of  the  same  kind  among  terrestrial  objects  ;  as  when  the 
shore  seems  to  the  mariner  to  recede,  as  he  rapidly  sails 


256  LETTERS  ON  ASTRONOMY. 

from  it ;  and  as  trees  and  other  objects  seem  to  glide  by 
us,  when,  on  riding  swiftly  past  them,  we  lose  the 
consciousness  of  our  own  motion.  He  was  also  smitten 
with  the  simplicity  prevalent  in  all  the  works  and  op- 
erations of  Nature,  which  is  more  and  more  conspicuous 
the  more  they  are  understood  ;  and  he  hence  concluded 
that  the  planets  do  not  move  in  the  complicated  paths 
which  most  preceding  astronomers  assigned  to  them.  I 
shall  explain  to  you,  hereafter,  the  details  of  his  system. 
I  need  only  at  present  remind  you  that  the  hypothesis 
which  he  espoused  and  defended,  (being  substantially 
the  same  as  that  proposed  by  Pythagoras,  five  hundred 
years  before  the  Christian  era,)  supposes,  first,  that  the 
apparent  movements  of  the  sun  by  day,  and  of  the  moon 
and  stars  by  night,  from  east  to  west,  result  from  the 
actual  revolution  of  the  earth  on  its  own  axis  from  west 
to  east ;  and,  secondly,  that  the  earth  and  all  the  planets 
revolve  about  the  sun  in  circular  orbits.  This  hypothe- 
sis, when  he  first  assumed  it,  was  with  him,  as  it  had 
been  with  Pythagoras,  little  more  than  mere  conjecture. 
The  arguments  by  which  its  truth  was  to  be  finally 
established  were  not  yet  developed,  and  could  not  be, 
without  the  aid  of  the  telescope,  which  was  not  yet  in- 
vented. Upon  this  hypothesis,  however,  he  set  out  to 
explain  all  the  phenomena  of  the  visible  heavens, — as 
the  diurnal  revolutions  of  the  sun,  moon,  and  stars,  the 
slow  progress  of  the  planets  through  the  signs  of  the  zo- 
diac, and  the  numerous  irregularities  to  which  the  plan- 
etary motions  are  subject.  These  last  are  apparently  so 
capricious, — being  for  some  time  forward,  then  station- 
ary, then  backward,  then  stationary  again,  and  finally 
direct,  a  second  time,  in  the  order  of  the  signs,  and  con- 
stantly varying  in  the  velocity  of  their  movements, — that 
nothing  but  long-continued  and  severe  meditation  could 
have  solved  all  these  appearances,  in  conformity  with  the 
idea  that  each  planet  is  pursuing  its  simple  way  all  the 
while  in  a  circle  around  the  sun.  Although,  therefore, 
Pythagoras  fathomed  the  profound  doctrine  that  the  sun 
is  the  centre  around  which  the  earth  and  all  the  planets 


COPERNICUS.  257 

revolve,  yet  we  have  no  evidence  that  he  ever  solved 
the  irregular  motions  of  the  planets  in  conformity  with 
his  hypothesis,  although  the  explanation  of  the  diurnal 
revolution  of  the  heavens,  by  that  hypothesis,  involved 
no  difficulty.  Ignorant  as  Copernicus  was  of  the  prin- 
ciple of  gravitation,  and  of  most  of  the  laws  of  motion, 
he  could  go  but  little  way  in  following  out  the  conse- 
quences of  his  own  hypothesis ;  and  all  that  can  be 
claimed  for  him  is,  that  he  solved,  by  means  of  it,  most 
of  the  common  phenomena  of  the  celestial  motions. 
He  indeed  got  upon  the  road  to  truth,  and  advanced 
some  way  in  its  sure  path ;  but  he  was  able  to  adduce 
but  few  independent  proofs,  to  show  that  it  was  the 
truth.  It  was  only  quite  at  the  close  of  his  life  that  he 
published  his  system  to  the  world,  and  that  only  at  the 
urgent  request  of  his  friends  ;  anticipating,  perhaps,  the 
opposition  of  a  bigoted  priesthood,  whose  ifury  was  af- 
terwards poured  upon  the  head  of  Galileo,  for  main- 
taining the  same  doctrines. 

Although,  therefore,  the  system  of  Copernicus  afford- 
ed an  explanation  of  the  celestial  motions,  far  more 
simple  and  rational  than  the  previous  systems  which 
made  the  earth  the  centre  of  those  motions,  yet  this 
fact  alone  was  not  sufficient  to  compel  the  assent  of 
astronomers ;  for  the  greater  part,  to  say  the  least,  of 
the  same  phenomena,  could  be  explained  on  either  hy- 
pothesis. With  the  old  doctrine  astronomers  were  al- 
ready familiar,  a  circumstance  which  made  it  seem  easi- 
er ;  while  the  new  doctrines  would  seem  more  difficult, 
from  their  being  imperfectly  understood.  Accordingly, 
for  nearly  a  century  after  the  publication  of  the  system  of 
Copernicus,  he  gained  few  disciples.  Tycho  Brahe  re- 
jected it,  and  proposed  one  of  his  own,  of  which  I  shall 
hereafter  give  you  some  account ;  and  it  would  proba- 
bly have  fallen  quite  into  oblivion,  had  not  the  obser- 
vations of  Galileo,  with  his  newly-invented  telescope, 
brought  to  light  innumerable  proofs  of  its  truth,  far  more 
cogent  than  any  which  Copernicus  himself  had  been 
able  to  devise. 

22* 


258  LETTERS   ON  ASTRONOMY. 

Galileo  no  sooner  had  completed  his  telescope,  and 
directed  it  to  the  heavens,  than  a  world  of  wonders  sud- 
denly burst  upon  his  enraptured  sight.  Pointing  it  to 
the  moon,  he  was  presented  with  a  sight  of  her  mottled 
disk,  and  of  her  mountains  and  valleys.  The  sun  ex- 
hibited his  spots ;  Venus,  her  phases ;  and  Jupiter,  his 
expanded  orb,  and  his  retinue  of  moons.  These  last 
he  named,  in  honor  of  his  patron,  Cosmo  d'Medici,  Med- 
icean  stars.  So  great  was  this  honor  deemed  of  asso- 
ciating one's  name  with  the  stars,  that  express  applica- 
tion was  made  to  Galileo,  by  the  court  of  France,  to 
award  this  distinction  to  the  reigning  Monarch,  Henry 
the  Fourth,  with  plain  intimations,  that  by  so  doing  he 
would  render  himself  and  his  family  rich  and  powerful 
for  ever. 

Galileo  published  the  result  of  his  discoveries  in  a  pa- 
per, denominated  '  Nuncius  Sidereus'  the  '  Messenger 
of  the  Stars.'  In  that  ignorant  and  marvellous  age,  this 
publication  produced  a  wonderful  excitement.  "  Many 
doubted,  many  positively  refused  to  believe,  so  novel  an 
announcement ;  all  were  struck  with  the  greatest  aston- 
ishment, according  to  their  respective  opinions,  either  at 
the  new  view  of  the  universe  thus  offered  to  them,  or  at 
the  high  audacity  of  Galileo,  in  inventing  such  fables." 
Even  Kepler,  the  great  German  astronomer,  of  whom  I 
shall  tell  you  more  by  and  by,  wrote  to  Galileo,  and  de- 
sired him  to  supply  him  with  arguments,  by  which  he 
might  answer  the  objections  to  these  pretended  discov- 
eries with  which  he  was  continually  assailed.  Galileo 
answered  him  as  follows :  "  In  the  first  place,  I  return 
you  my  thanks  that  you  first,  and  almost  alone,  before 
the  question  had  been  sifted,  (such  is  your  candor,  and 
the  loftiness  of  your  mind,)  put  faith  in  my  assertions. 
You  tell  me  you  have  some  telescopes,  but  not  sufficient- 
ly good  to  magnify  distant  objects  with  clearness,  and 
that  you  anxiously  expect  a  sight  of  mine,  which  mag- 
nifies images  more  than  a  thousand  times.  It  is  mine 
no  longer,  for  the  Grand  Duke  of  Tuscany  has  asked  it 
of  me,  and  intends  to  lay  it  up  in  his  museum,  among 


GALILEO.  259 

his  most  rare  and  precious  curiosities,  in  eternal  remem- 
brance of  the  invention. 

"  You  ask,  my  dear  Kepler,  for  other  testimonies.  I 
produce,  for  one,  the  Grand  Duke,  who,  after  observing 
the  Medicean  planets  several  times  with  me  at  Pisa, 
during  the  last  months,  made  me  a  present,  at  parting, 
of  more  than  a  thousand  florins,  and  has  now  invited 
me  to  attach  myself  to  him,  with  the  annual  salary  of  one 
thousand  florins,  and  with  the  title  of  '  Philosopher  and 
Principal  Mathematician  to  His  Highness  ;'  without  the 
duties  of  any  office  to  perform,  but  with  the  most  com- 
plete leisure.  I  produce,  for  another  witness,  myself, 
who,  although  already  endowed  in  this  College  with  the 
noble  salary  of  one  thousand  florins,  such  as  no  profes- 
sor of  mathematics  ever  before  received,  and  which  I 
might  securely  enjoy  during  my  life,  even  if  these  plan- 
ets should  deceive  me  and  should  disappear,  yet  quit 
this  situation,  and  take  me  where  want  and  disgrace 
will  be  my  punishment,  should  I  prove  to  have  been 
mistaken." 

The  learned  professors  in  the  universities,  who,  in 
those  days,  were  unaccustomed  to  employ  their  senses 
in  inquiring  into  the  phenomena  of  Nature,  but  satisfied 
themselves  with  the  authority  of  Aristotle,  on  all  sub- 
jects, were  among  the  most  incredulous  with  respect  to 
the  discoveries  of  Galileo.  "  Oh,  my  dear  Kepler," 
says  Galileo,  "  how  I  wish  that  we  could  have  one 
hearty  laugh  together.  Here,  at  Padua,  is  the  princi- 
pal Professor  of  Philosophy,  whom  I  have  repeatedly 
and  urgently  requested  to  look  at  the  moon  and  planets 
through  my  glass,  which  he  pertinaciously  refuses  to  do. 
Why  are  you  not  here  ?  What  shouts  of  laughter  we 
should  have  at  this  glorious  folly,  and  to  hear  the  Pro- 
fessor of  Philosophy  at  Pisa  laboring  before  the  Grand 
Duke,  with  logical  arguments,  as  if  with  magical  incan- 
tations, to  charm  the  new  planets  out  of  the  sky." 

The  following  argument  by  Sizzi,  a  contemporary 
astronomer  of  some  note,  to  prove  that  there  can  be 
only  seven  planets,  is  a  specimen  of  the  logic  with 


260  LETTERS  ON  ASTRONOMY. 

which  Galileo  was  assailed.  "  There  are  seven  win- 
dows given  to  animals  in  the  domicile  of  the  head, 
through  which  the  air  is  admitted  to  the  tabernacle  of 
the  body,  to  enlighten,  to  warm,  and  to  nourish  it ; 
which  windows  are  the  principal  parts  of  the  microcosm, 
or  little  world, — two  nostrils,  two  eyes,  two  ears,  and 
one  mouth.  So  in  the  heavens,  as  in  a  macrocosm,  or 
great  world,  there  are  two  favorable  stars,  Jupiter  and 
Venus ;  two  unpropitious,  Mars  and  Saturn  ;  two  lu- 
minaries, the  Sun  and  Moon ;  and  Mercury  alone,  un- 
decided and  indifferent.  From  which,  and  from  many 
other  phenomena  of  Nature,  such  as  the  seven  metals, 
&c.,  which  it  were  tedious  to  enumerate,  we  gather 
that  the  number  of  planets  is  necessarily  seven.  More- 
over, the  satellites  are  invisible  to  the  naked  eye,  and 
therefore  can  exercise  no  influence  over  the  earth,  and 
therefore  would  be  useless,  and  therefore  do  not  exist. 
Besides,  as  well  the  Jews  and  other  ancient  nations,  as 
modern  Europeans,  have  adopted  the  division  of  the 
week  into  seven  days,  and  have  named  them  from  the 
seven  planets.  Now,  if  we  increase  the  number  of 
planets,  this  whole  system  falls  to  the  ground." 

When,  at  length,  the  astronomers  of  the  schools 
found  it  useless  to  deny  the  fact  that  Jupiter  is  attend- 
ed by  smaller  bodies,  which  revolve  around  him,  they 
shifted  their  ground  of  warfare,  and  asserted  that  Gali- 
leo had  not  told  the  whole  truth ;  that  there  were  not 
merely  four  satellites,  but  a  still  greater  number ;  one 
said  five  ;  another,  nine  ;  and  another,  twelve  ;  but,  in  a 
little  time,  Jupiter  moved  forward  in  his  orbit,  and  left 
all  behind  him,  save  the  four  Medicean  stars. 

It  had  been  objected  to  the  Copernican  system,  that 
were  Venus  'a  body  which  revolved  around  the  sun  in 
an  orbit  interior  to  that  of  the  earth,  she  would  undergo 
changes  similar  to  those  of  the  moon.  As  no  such 
changes  could  be  detected  by  the  naked  eye,  no  satis- 
factory answer  could  be  given  to  this  objection  ;  but 
the  telescope  set  all  right,  by  showing,  in  fact,  the  pha- 
ses of  Venus.  The  same  instrument  disclosed,  also,  in 


GALILEO.  261 

the  system  of  Jupiter  and  his  moons,  a  miniature  exhi- 
bition of  the  solar  system  itself.  It  showed  the  actual 
existence  of  the  motion  of  a  number  of  bodies  around 
one  central  orb,  exactly  similar  to  that  which  was  pred- 
icated of  the  sun  and  planets.  Every  one,  therefore, 
of  these  new  and  interesting  discoveries,  helped  to  con- 
firm the  truth  of  the  system  of  Copernicus. 

But  a  fearful  cloud  was  now  rising  over  Galileo,  which 
spread  itself,  and  grew  darker  every  hour.  The  Church 
of  Rome  had  taken  alarm  at  the  new  doctrines  respect- 
ing the  earth's  motion,  as  contrary  to  the  declarations 
of  the  Bible,  and  a  formidable  difficulty  presented  it- 
self, namely,  how  to  publish  and  defend  these  doctrines, 
without  invoking  the  terrible  punishments  inflicted  by 
the  Inquisition  on  heretics.  No  work  could  be  printed 
without  license  from  the  court  of  Rome  ;  and  any  opin- 
ions supposed  to  be  held  and  much  more  known  to 
be  taught  by  any  one,  which,  by  an  ignorant  and  su- 
perstitious priesthood,  could  be  interpreted  as  contrary 
to  Scripture,  would  expose  the  offender  to  the  sever- 
est punishments,  even  to  imprisonment,  scourging,  and 
death.  We,  who  live  in  an  age  so  distinguished  for 
freedom  of  thought  and  opinion,  can  form  but  a  very 
inadequate  conception  of  the  bondage  in  which  the 
minds  of  men  were  held  by  the  chains  of  the  Inquisi- 
tion. It  was  necessary,  therefore,  for  Galileo  to  pro- 
ceed with  the  greatest  caution  in  promulgating  truths 
which  his  own  discoveries  had  confirmed.  He  did  not, 
like  the  Christian  martyrs,  proclaim  the  truth  in  the 
face  of  persecutions  and  tortures ;  but  while  he  sought 
to  give  currency  to  the  Copernican  doctrines,  he  labor- 
ed, at  the  same  time,  by  cunning  artifices,  to  blind  the 
ecclesiastics  to  his  real  designs,  and  thus  to  escape  the 
effects  of  their  hostility. 

Before  Galileo  published  his  doctrines  in  form,  he  had 
expressed  himself  so  freely,  as  to  have  excited  much 
alarm  among  the  ecclesiastics.  One  of  them  preached 
publicly  against  him,  taking  for  his  text,  the  passage, 
"  Ye  men  of  Galilee,  why  stand  ye  here  gazing  up  into 


262  LETTERS  ON  ASTRONOMY. 

heaven  ?"  He  therefore  thought  it  prudent  to  resort  to 
Rome,  and  confront  his  enemies  face  to  face.  A  con- 
temporary describes  his  appearance  there  in  the  follow- 
ing terms,  in  a  letter  addressed  to  a  Romish  Cardinal : 
"  Your  Eminence  would  be  delighted  with  Galileo,  if 
you  heard  him  holding  forth,  as  he  often  does,  in  the 
midst  of  fifteen  or  twenty,  all  violently  attacking  him, 
sometimes  in  one  house,  sometimes  in  another.  But 
he  is  armed  after  such  fashion,  that  he  laughs  all  of 
them  to  scorn ;  and  even  if  the  novelty  of  his  opinions 
prevents  entire  persuasion,  at  least  he  convicts  of  emp- 
tiness most  of  the  arguments  with  which  his  adversaries 
endeavor  to  overwhelm  him." 

In  1616,  Galileo,  as  he  himself  states,  had  a  most 
gracious  audience  of  the  Pope,  Paul  the  Fifth,  which 
lasted  for  nearly  an  hour,  at  the  end  of  which  his  Holi- 
ness assured  him,  that  the  Congregation  were  no  longer 
in  a  humor  to  listen  lightly  to  calumnies  against  him, 
and  that  so  long  as  he  occupied  the  Papal  chair,  Gali- 
leo might  think  himself  out  of  all  danger.  Neverthe- 
less, he  was  not  allowed  to  return  home,  without  receiv- 
ing formal  notice  not  to  teach  the  opinions  of  Coper- 
nicus, "  that  the  sun  is  in  the  centre  of  the  system,  and 
that  the  earth  moves  about  it,"  from  that  time  forward, 
in  any  manner. 

Galileo  had  a  most  sarcastic  vein,  and  often  rallied 
his  persecutors  with  the  keenest  irony.  This  he  ex- 
hibited, some  time  after  quitting  Rome,  in  an  epistle 
which  he  sent  to  the  Arch  Duke  Leopold,  accompany- 
ing his 'Theory  of  the  Tides.'  "This  theory,"  says 
he,  "  occurred  to  me  when  in  Rome,  whilst  the  the- 
ologians were  debating  on  the  prohibition  of  Coperni- 
cus's  book,  and  of  the  opinion  maintained  in  it  of  the 
motion  of  the  earth,  which  I  at  that  time  believed  ;  un- 
til it  pleased  those  gentlemen  to  suspend  the  book,  and 
to  declare  the  opinion  false  and  repugnant  to  the  Holy 
Scriptures.  Now,  as  I  know  how  well  it  becomes  me 
to  obey  and  believe  the  decisions  of  my  superiors,  which 
proceed  out  of  more  profound  knowledge  than  the 


GALILEO.  263 

weakness  of  my  intellect  can  attain  to,  this  theory, 
which  I  send  you,  which  is  founded  on  the  motion  of 
the  earth,  I  now  look  upon  as  a  fiction  and  a  dream, 
and  beg  your  Highness  to  receive  it  as  such.  But,  as 
poets  often  learn  to  prize  the  creations  of  their  fancy, 
so,  in  like  manner,  do  I  set  some  value  on  this  absurdi- 
ty of  mine.  It  is  true,  that  when  I  sketched  this  little 
work,  I  did  hope  that  Copernicus  would  not,  after  eigh- 
ty years,  be  convicted  of  error ;  and  I  had  intended  to 
develope  atad  amplify  it  further  ;  but  a  voice  from  heav- 
en suddenly  awakened  me,  and  at  once  annihilated  all 
my  confused  and  entangled  fancies." 

It  is  difficult,  however,  sometimes  to  decide  wheth- 
er the  language  of  Galileo  is  ironical,  or  whether  he 
uses  it  with  subtlety,  with  the  hope  of  evading  the 
anathemas  of  the  Inquisition.  Thus  he  ends  one  of  his 
writings  with  the  following  passage :  "In  conclusion, 
since  the  motion  attributed  to  the  earth,  which  I,  as  a 
pious  and  Catholic  person,  consider  most  false,  and  not 
to  exist,  accommodates  itself  so  well  to  explain  so  many 
and  such  different  phenomena,  I  shall  not  feel  sure  that, 
false  as  it  is,  it  may  not  just  as  deludingly  correspond 
with  the  phenomena  of  comets." 

In  the  year  1624,  soon  after  the  accession  of  Ur- 
ban the  Eighth  to  the  Pontifical  chair,  Galileo  went  to 
Rome  again,  to  offer  his  congratulations  to  the  new 
Pope,  as  well  as  to  propitiate  his  favor.  He  seems  to 
have  been  received  with  unexpected  cordiality ;  and,  on 
his  departure,  the  Pope  commended  him  to  the  good 
graces  of  Ferdinand,  Grand  Duke  of  Tuscany,  in  the 
following  terms :  "  We  find  in  him  not  only  literary 
distinction,  but  also  the  love  of  piety,  and  he  is  strong 
in  those  qualities  by  which  Pontifical  good-will  is  easily 
obtained.  And  now,  when  he  has  been  brought  to  this 
city,  to  congratulate  Us  on  Our  elevation,  We  have  lov- 
ingly embraced  him ;  nor  can  We  suffer  him  to  return 
to  the  country  whither  your  liberality  recalls  him,  with- 
out an  ample  provision  of  Pontifical  love.  And  that  you 
may  know  how  dear  he  is  to  Us,  we  have  willed  to  give 


264  LETTERS  ON  ASTRONOMY. 

him  this  honorable  testimonial  of  virtue  and  piety. 
And  We  further  signify,  that  every  benefit  which  you 
shall  confer  upon  him  will  conduce  to  Our  gratification." 

In  the  year  1630,  Galileo  finished  a  great  work,  on 
which  he  had  been  long  engaged,  entitled,  '  The  Dia- 
logue on  the  Ptolemaic  and  Copernican  Systems/ 
From  the  notion  which  prevailed,  that  he  still  counte- 
nanced the  Copernican  doctrine  of  the  earth's  motion, 
which  had  been  condemned  as  heretical,  it  was  some 
time  before  he  could  obtain  permission  from  the  Inquis- 
itors (whose  license  was  necessary  to  every  book)  to 
publish  it.  This  he  was  able  to  do,  only  by  employing 
again  that  duplicity  or  artifice  which  would  throw  dust 
in  the  eyes  of  the  vain  and  superstitious  priesthood. 
In  1632,  the  work  appeared  under  the  following  title : 
'  A  Dialogue,  by  Galileo  Galilei,  Extraordinary  Mathe- 
matician of  the  University  of  Pisa,  and  Principal  Phi- 
losopher and  Mathematician  of  the  Most  Serene  Grand 
Duke  of  Tuscany  ;  in  which,  in  a  Conversation  of  four 
days,  are  discussed  the  two  principal  Systems  of  the 
World,  the  Ptolemaic  and  Copernican,  indeterminately 
proposing  the  Philosophical  Arguments  as  well  on  one 
side  as  on  the  other.'  The  subtle  disguise  which  he 
wore,  may  be  seen  from  the  following  extract  from  his 
'  Introduction,'  addressed  '  To  the  discreet  Reader.' 

"  Some  years  ago,  a  salutary  edict  was  promulgated 
at  Rome,  which,  in  order  to  obviate  the  perilous  scan- 
dals of  the  present  age,  enjoined  an  opportune  silence 
on  the  Pythagorean  opinion  of  the  earth's  motion. 
Some  were  not  wanting,  who  rashly  asserted  that  this 
decree  originated,  not  in  a  judicious  examination,  but 
in  ill-informed  passion;  and  complaints  were  heard, 
that  counsellors  totally  inexperienced  in  astronomical 
observations  ought  not,  by  hasty  prohibitions,  to  clip 
the  wings  of  speculative  minds.  My  zeal  could  not 
keep  silence  when  I  heard  these  rash  lamentations,  and 
I  thought  it  proper,  as  being  fully  informed  with  regard 
to  that  most  prudent  determination,  to  appear  publicly 
on  the  theatre  of  the  world,  as  a  witness  of  the  actual 


GALILEO.  265 

truth.  I  happened  at  that  time  to  be  in  Rome  :  I  was 
admitted  to  the  audiences,  and  enjoyed  the  approbation, 
of  the  most  eminent  prelates  of  that  court ;  nor  did  the 
publication  of  that  decree  occur  without  my  receiving 
some  prior  intimation  of  it.  Wherefore,  it  is  my  inten- 
tion, in  this  present  work,  to  show  to  foreign  nations, 
that  as  much  is  known  of  this  matter  in  Italy,  and 
particularly  in  Rome,  as  ultramontane  diligence  can 
ever  have  formed  any  notion  of,  and  collecting  together 
all  my  own  speculations  on  the  Copernican  system,  to 
give  them  to  understand  that  the  knowledge  of  all  these 
preceded  the  Roman  censures ;  and  that  from  this 
country  proceed  not  only  dogmas  for  the  salvation  of 
the  soul,  but  also  ingenious  discoveries  for  the  gratifi- 
cation of  the  understanding.  With  this  object,  I  have 
taken  up  in  the  '  Dialogue'  the  Copernican  side  of  the 
question,  treating  it  as  a  pure  mathematical  hypothesis  ; 
and  endeavoring,  in  every  artificial  manner,  to  repre- 
sent it  as  having  the  advantage,  not  over  the  opinion 
of  the  stability  of  the  earth  absolutely,  but  according  to 
the  manner  in  which  that  opinion  is  defended  by  some, 
who  indeed  profess  to  be  Aristotelians,  but  .retain  only 
the  name,  and  are  contented,  without  improvement,  to 
worship  shadows,  not  philosophizing  with  their  own 
reason,  but  only  from  the  recollection  of  the  four  prin- 
ciples imperfectly  understood." 

Although  the  Pope  himself,  as  well  as  the  Inquisitors, 
had  examined  Galileo's  manuscript,  and,  not  having  the 
sagacity  to  detect  the  real  motives  of  the  author,  had 
consented  to  its  publication,  yet,  when  the  book  was 
out,  the  enemies  of  Galileo  found  means  to  alarm  the 
court  of  Rome,  and  Galileo  was  summoned  to  appear 
before  the  Inquisition.  The  philosopher  was  then  sev- 
enty years  old,  and  very  infirm,  and  it  was  with  great 
difficulty  that  he  performed  the  journey.  His  unequal- 
led dignity  and  celebrity,  however,  commanded  the  in- 
voluntary respect  of  the  tribunal  before  which  he  was 
summoned,  which  they  manifested  by  permitting  him 
to  reside  at  the  palace  of  his  friend,  the  Tuscan  Am- 
23  L.  A. 


266  LETTERS  ON  ASTRONOMY 

bassador  ;  and  when  it  became  necessary,  in  the  course 
of  the  inquiry,  to  examine  him  in  person,  although  his 
removal  to  the  Holy  Office  was  then  insisted  upon,  yet 
he  was  not,  like  other  heretics,  committed  to  close  and 
solitary  confinement.  On  the  contrary,  he  was  lodged 
in  the  apartments  of  the  Head  of  the  Inquisition,  where 
he  was  allowed  the  attendance  of  his  own  servant,  who 
was  also  permitted  to  sleep  in  an  adjoining  room,  and 
to  come  and  go  at  pleasure.  These  were  deemed  ex- 
traordinary indulgences  in  an  age  when  the  punishment 
of  heretics  usually  began  before  their  trial. 

About  four  months  after  Galileo's  arrival  in  Rome, 
he  was  summoned  to  the  Holy  Office.  He  was  detain- 
ed there  during  the  whole  of  that  day  ;  and  on  the 
next  day  was  conducted,  in  a  penitential  dress,  to  the 
Convent  of  Minerva,  where  the  Cardinals  and  Prelates, 
his  judges,  were  assembled  for  the  purpose  of  passing 
judgement  upon  him,  by  which  this  venerable  old  man 
was  solemnly  called  upon  to  renounce  and  abjure,  as 
impious  and  heretical,  the  opinions  which  his  whole  ex- 
istence had  been  consecrated  to  form  and  strengthen. 
Probably  there  is  not  a  more  curious  document  in  the 
history  of  science,  than  that  which  contains  the  sen- 
tence of  the  Inquisition  on  Galileo,  and  his  consequent 
abjuration.  It  teaches  us  so  much,  both  of  the  dark- 
ness and  bigotry  of  the  terrible  Inquisition,  and  of  the 
sufferings  encountered  by  those  early  martyrs  of  sci- 
ence, that  I  will  transcribe  for  your  perusal,  from  the 
excellent  'Life  of  Galileo'  in  the  'Library  of  Useful 
Knowledge,'  (from  which  I  have  borrowed  much  alrea- 
dy,) the  entire  record  of  this  transaction.  The  sen- 
tence of  the  Inquisition  is  as  follows : 

"  We,  the  undersigned,  by  the  grace  of  God,  Cardi- 
nals of  the  Holy  Roman  Church,  Inquisitors  General 
throughout  the  whole  Christian  Republic,  Special  Depu- 
ties of  the  Holy  Apostolical  Chair  against  heretical  de- 
pravity : 

"  Whereas,  you,  Galileo,  son  of  the  late  Vincenzo 
Galilei  of  Florence,  aged  seventy  years,  were  denoun- 


<3ALILEO.  267 

ced  in  1615,  to  this  Holy  Office,  for  holding  as  true  a 
false  doctrine  taught  by  many,  namely,  that  the  sun  is 
immovable  in  the  centre  of  the  world,  and  that  the 
earth  moves,  and  also  with  a  diurnal  motion ;  also,  for 
having  pupils  which  you  instructed  in  the  same  opin- 
ions; also,  for  maintaining  a  correspondence  on  the 
same  with  some  German  mathematicians ;  also,  for 
publishing  certain  letters  on  the  solar  spots,  in  which 
you  developed  the  same  doctrine  as  true ;  also,  for  an- 
swering the  objections  which  were  continually  produced 
from  the  Holy  Scriptures,  by  glozing  the  said  Scriptures, 
according  to  your  own  meaning ;  and  whereas,  thereupon 
was  produced  the  copy  of  a  writing,  in  form  of  a  letter, 
professedly  written  by  you  to  a  person  formerly  your 
pupil,  in  which,  following  the  hypothesis  of  Copernicus, 
you  include  several  propositions  contrary  to  the  true 
sense  and  authority  of  the  Holy  Scriptures :  therefore, 
this  Holy  Tribunal,  being  desirous  of  providing  against 
the  disorder  and  mischief  which  was  thence  proceeding 
and  increasing,  to  the  detriment  of  the  holy  faith,  by 
the  desire  of  His  Holiness,  and  of  the  Most  Eminent 
Lords  Cardinals  of  this  supreme  and  universal  Inquisi- 
tion, the  two  propositions  of  the  stability  of  the  sun,  and 
motion  of  the  earth,  were  qualified  by  the  Theological 
Qualifiers,  as  follows: 

"  1.  The  proposition  that  the  sun  is  in  the  centre  of 
the  world,  and  immovable  from  its  place,  is  absurd,  phi- 
losophically false,  and  formally  heretical ;  because  it  is 
expressly  contrary  to  the  Holy  Scriptures. 

"  2.  The  proposition  that  the  earth  is  not  the  centre 
of  the  world,  nor  immovable,  but  that  it  moves,  and 
also  with  a  diurnal  motion,  is  also  absurd,  philosophi- 
cally false,  and,  theologically  considered,  equally  errone- 
ous in  faith. 

"  But  whereas,  being  pleased  at  that  time  to  deal 
mildly  with  you,  it  was  decreed  in  the  Holy  Congrega- 
tion, held  before  His  Holiness  on  the  twenty-fifth  day 
of  February,  1616,  that  His  Eminence  the  Lord  Cardi- 
nal Bellannine  should  enjoin  you  to  give  up  altogether 


268  LETTERS  ON  ASTRONOMY. 

the  said  false  doctrine  ;  if  you  should  refuse,  that  you 
should  be  ordered  by  the  Commissary  of  the  Holy  Office 
to  relinquish  it,  not  to  teach  it  to  others,  nor  to  defend 
it,  and  in  default  of  the  acquiescence,  that  you  should 
be  imprisoned ;  and  in  execution  of  this  decree,  on  the 
following  day,  at  the  palace,  in  presence  of  His  Emi- 
nence the  said  Lord  Cardinal  Bellarmine,  after  you  had 
been  mildly  admonished  by  the  said  Lord  Cardinal, 
you  were  commanded  by  the  acting  Commissary  of  the 
Holy  Office,  before  a  notary  and  witnesses,  to  relinquish 
altogether  the  said  false  opinion,  and  in  future  neither 
to  defend  nor  teach  it  in  any  manner,  neither  verbally 
nor  in  writing,  and  upon  your  promising  obedience,  you 
were  dismissed. 

"  And,  in  order  that  so  pernicious  a  doctrine  might  be 
altogether  rooted  out,  nor  insinuate  itself  further  to  the 
heavy  detriment  of  the  Catholic  truth,  a  decree  emana- 
ted from  the  Holy  Congregation  of  the  Index,  prohibit- 
ing the  books  which  treat  of  this  doctrine  ;  and  it  was 
declared  false,  and  altogether  contrary  to  the  Holy  and 
Divine  Scripture. 

"  And  whereas,  a  book  has  since  appeared,  published 
at  Florence  last  year,  the  title  of  which  showed  that  you 
were  the  author,  which  title  is,  '  The  Dialogue  of  Gali- 
leo Galilei,  on  the  two  principal  Systems  of  the  World, 
the  Ptolemaic  and  Copernican ;'  and  whereas,  the  Holy 
Congregation  has  heard  that,  in  consequence  of  printing 
the  said  book,  the  false  opinion  of  the  earth's  motion 
and  stability  of  the  sun  is  daily  gaining  ground  ;  the 
said  book  has  been  taken  into  careful  consideration, 
and  in  it  has  been  detected  a  glaring  violation  of  the 
said  order,  which  had  been  intimated  to  you ;  inasmuch 
as  in  this  book  you  have  defended  the  said  opinion,  al- 
ready, and  in  your  presence,  condemned ;  although  in 
the  said  book  you  labor,  with  many  circumlocutions,  to 
induce  the  belief  that  it  is  left  by  you  undecided,  and  in 
express  terms  probable  ;  which  is  equally  a  very  grave 
error,  since  an  opinion  can  in  no  way  be  probable  which 
has  been  already  declared  and  finally  determined  con- 


CALILEO.  269 

trary  to  the  Divine  Scripture.  Therefore,  by  Our  order, 
you  have  been  cited  to  this  Holy  Office,  where,  on  your 
examination  upon  oath,  you  have  acknowledged  the  said 
book  as  written  and  printed  by  you.  You  also  confessed 
that  you  began  to  write  the  said  book  ten  or  twelve 
years  ago,  after  the  order  aforesaid  had  been  given. 
Also,  that  you  demanded  license  to  publish  it,  but  with- 
out signifying  to  those  who  granted  you  this  permission, 
that  you  had  been  commanded  not  to  hold,  defend,  or 
teach,  the  said  doctrine  in  any  manner.  You  also  con- 
fessed, that  the  style  of  said  book  was,  in  many  places, 
so  composed,  that  the  reader  might  think  the  arguments 
adduced  on  the  false-side  to  be  so  worded,  as  more  effec- 
tually to  entangle  the  understanding  than  to  be  easily 
solved,  alleging,  in  excuse,  that  you  have  thus  run  into 
an  error,  foreign  (as  you  say)  to  your  intention,  from 
writing  in  the  form  of  a  dialogue,  and  in  consequence 
of  the  natural  complacency  which  every  one  feels  with 
regard  to  his  own  subtilties,  and  in  showing  himself 
more  skilful  than  the  generality  of  mankind  in  contriv- 
ing, even  in  favor  of  false  propositions,  ingenious  and 
apparently  probable  arguments. 

"  And,  upon  a  convenient  time  being  given  you  for 
making  your  defence,  you  produced  a  certificate  in 
the  handwriting  of  His  Eminence,  the  Lord  Cardinal 
Bellarmine,  procured,  as  you  said,  by  yourself,  that  you 
might  defend  yourself  against  the  calumnies  of  your  ene- 
mies, who  reported  that  you  had  abjured  your  opinions, 
and  had  been  punished  by  the  Holy  Office ;  in  which 
certificate  it  is  declared,  that  you  had  not  abjured,  nor 
had  been  punished,  but  merely  that  the  declaration  made 
by  his  Holiness,  and  promulgated  by  the  Holy  Congre- 
gation of  the  Index,  had  been  announced  to  you,  which 
declares  that  the  opinion  of  the  motion  of  the  earth,  and 
stability  of  the  sun,  is  contrary  to  the  Holy  Scriptures, 
and  therefore  cannot  be  held  or  defended.  Wherefore, 
since  no  mention  is  there  made  of  two  articles  of  the 
order,  to  wit,  the  order  *  not  to  teach,'  and  '  in  any  man- 
ner,' you  argued  that  we  ought  to  believe  that,  in  the 
23* 


270  LETTERS  ON  ASTRONOMY. 

lapse  of  fourteen  or  sixteen  years,  they  had  escaped 
your  memory,  and  that  this  was  also  the  reason  why 
you  were  silent  as  to  the  order,  when  you  sought  per- 
mission to  publish  your  book,  and  that  this  is  said  by 
you,  not  to  excuse  your  error,  but  that  it  may  be  attrib- 
uted to  vain-glorious  ambition  rather  than  to  malice. 
But  this  very  certificate,  produced  on  your  behalf,  has 
greatly  aggravated  your  offence,  since  it  is  therein  de- 
clared, that  the  said  opinion  is  contrary  to  the  Holy 
Scriptures,  and  yet  you  have  dared  to  treat  of  it,  and  to 
argue  that  it  is  probable ;  nor  is  there  any  extenuation 
in  the  license  artfully  and  cunningly  extorted  by  you, 
since  you  did  not  intimate  the  command  imposed  upon 
y,ou.  But  whereas,  it  appeared  to  Us  that  you  had  not 
disclosed  the  whole  truth  with  regard  to  your  intentions, 
We  thought  it  necessary  to  proceed  to  the  rigorous  ex- 
amination of  you,  in  which  (without  any  prejudice  to 
what  you  had  confessed,  and  which  is  above  detailed 
against  you,  with  regard  to  your  said  intention)  you  an- 
swered like  a  good  Catholic. 

"Therefore,  having  seen  and  maturely  considered 
the  merits  of  your  cause,  with  your  said  confessions 
and  excuses,  and  every  thing  else  which  ought  to  be 
seen  and  considered,  We  have  come  to  the  underwrit- 
ten final  sentence  against  you  : 

"  Invoking,  therefore,  the  most  holy  name  of  our 
Lord  Jesus  Christ,  and  of  his  Most  Glorious  Virgin 
Mother,  Mary,  by  this  Our  final  sentence,  which,  sitting 
in  council  and  judgement  for  the  tribunal  of  the  Rever- 
end Masters  of  Sacred  Theology,  and  Doctors  of  both 
Laws,  Our  Assessors,  We  put  forth  in  this  writing 
touching  the  matters  and  controversies  before  Us,  be- 
tween the  Magnificent  Charles  Sincerus,  Doctor  of  both 
Laws,  Fiscal  Proctor  of  this  Holy  Office,  of  the  one  part, 
and  you,  Galileo  Galilei,  an  examined  and  confessed 
criminal  from  this  present  writing  now  in  progress,  as 
above,  of  the  other  part,  We  pronounce,  judge,  and 
declare,  that  you,  the  said  Galileo,  by  reason  of  these 
things  which  have  been  detailed  in  the  course  of  this 


GALILEO.  271 

writing,  and  which,  as  above,  you  have  confessed,  have 
rendered  yourself  vehemently  suspected,  by  this  Holy 
Office,  of  heresy ;  that  is  to  say,  that  you  believe  and 
hold  the  false  doctrine,  and  contrary  to  the  Holy  and 
Divine  Scriptures,  namely,  that  the  sun  is  the  centre  of 
the  world,  and  that  it  does  not  move  from  east  to  west, 
and  that  the  earth  does  move,  and  is  not  the  centre  of 
the  world ;  also,  that  an  opinion  can  be  held  and  sup- 
ported, as  probable,  after  it  has  been  declared  and  final- 
ly decreed  contrary  to  the  Holy  Scripture,  and  conse- 
quently, that  you  have  incurred  all  the  censures  and 
penalties  enjoined  and  promulgated  in  the  sacred  can- 
ons, and  other  general  and  particular  constitutions 
against  delinquents  of  this  description.  From  which  it 
is  Our  pleasure  that  you  be  absolved,  provided  that, 
with  a  sincere  heart  and  unfeigned  faith,  in  Our  pres- 
ence, you  abjure,  curse,  and  detest,  the  said  errors  and 
heresies,  and  every  other  error  and  heresy,  contrary  to 
the  Catholic  and  Apostolic  Church  of  Rome,  in  the 
form  now  shown  to  you. 

"  But  that  your  grievous  and  pernicious  error  and 
transgression  may  not  go  altogether  unpunished,  and 
that  you  may  be  made  more  cautious  in  future,  and 
may  be  a  warning  to  others  to  abstain  from  delinquen- 
cies of  this  sort,  We  decree,  that  the  book  of  the  Dia- 
logues of  Galileo  Galilei  be  prohibited  by  a  public  edict, 
and  We  condemn  you  to  the  formal  prison  of  this  Holy 
Office  for  a  period  determinable  at  Our  pleasure ;  and, 
by  way  of  salutary  penance,  We  order  you,  during  the 
next  three  years,  to  recite,  once  a  week,  the  seven  peni- 
tential psalms,  reserving  to  Ourselves  the  power  of  mod- 
erating, commuting,  or  taking  off  the  whole  or  part  of 
the  said  punishment,  or  penance. 

"  And  so  We  say,  pronounce,  and  by  Our  sentence 
declare,  decree,  and  reserve,  in  this  and  in  every  other 
better  form  and  manner,  which  lawfully  We  may  and 
can  use.  So  We,  the  subscribing  Cardinals,  pro- 
nounce." [Subscribed  by  seven  Cardinals.] 

In  conformity  with  the  foregoing  sentence,  Galileo 


LETTERS  ON  ASTRONOMY. 

was  made  to  kneel  before  the  Inquisition,  and  make  the 
following  Abjuration  : 

"  I,  Galileo  Galilei,  son  of  the  late  Vincenzo  Galilei, 
of  Florence,  aged  seventy  years,  being  brought  person- 
ally to  judgement,  and  kneeling  before  you,  Most  Emi- 
nent and  Most  Reverend  Lords  Cardinals,  General  In- 
quisitors of  the  Universal  Christian  Republic  against 
heretical  depravity,  having  before  my  eyes  the  Holy 
Gospels,  which  I  touch  with  my  own  hands,  swear,  that 
I  have  always  believed,  and  with  the  help  of  God  will 
in  future  believe,  every  article  which  the  Holy  Catho- 
lic and  Apostolic  Church  of  Rome  holds,  teaches,  and 
preaches.  But  because  I  had  been  enjoined,  by  this 
Holy  Office,  altogether  to  abandon  the  false  opinion 
which  maintains  that  the  sun  is  the  centre  and  immov- 
able, and  forbidden  to  hold,  defend,  or  teach,  the  said 
false  doctrine,  in  any  manner ;  and  after  it  had  been 
signified  to  me  that  the  said  doctrine  is  repugnant  to 
the  Holy  Scripture,  I  have  written  and  printed  a  book, 
in  which  I  treat  of  the  same  doctrine  now  condemned, 
and  adduce  reasons  with  great  force  in  support  of  the 
same,  without  giving  any  solution,  and  therefore  have 
been  judged  grievously  suspected  of  heresy ;  that  is  to 
say,  that  I  held  and  believed  that  the  sun  is  the  centre 
of  the  world  and  immovable,  and  that  the  earth  is  not 
the  centre  and  movable ;  willing,  therefore,  to  remove 
from  the  minds  of  Your  Eminences,  and  of  every  Cath- 
olic Christian,  this  vehement  suspicion  rightfully  enter- 
tained towards  me,  with  a  sincere  heart  and  unfeigned 
faith,  I  abjure,  curse,  and  detest,  the  said  errors  and 
heresies,  and  generally  every  other  error  and  sect  con- 
trary to  the  said  Holy  Church  ;  and  I  swear,  that  I  will 
never  more  in  future  say  or  assert  any  thing,  verbally  or 
in  writing,  which  may  give  rise  to  a  similar  suspicion  of 
me :  but  if  I  shall  know  any  heretic,  or  any  one  sus- 
pected of  heresy,  that  I  will  denounce  him  to  this  Holy 
Office,  or  to  the  Inquisitor  and  Ordinary  of  the  place 
in  which  I  may  be.  I  swear,  moreover,  and  promise, 
that  I  will  fulfil  and  observe  fully,  all  the  penances 


GALILEO.  273 

which  have  been  or  shall  be  laid  on  me  by  this  Holy 
Office.  But  if  it  shall  happen  that  I  violate  any  of 
my  said  promises,  oaths,  and  protestations,  (which  God 
avert !)  I  subject  myself  to  all  the  pains  and  punish- 
ments which  have  been  decreed  and  promulgated  by 
the  sacred  canons,  and  other  general  and  particular 
constitutions,  against  delinquents  of  this  description. 
So  may  God  help  me,  and  his  Holy  Gospels,  which  I 
touch  with  my  own  hands.  I,  the  above-named  Galileo 
Galilei,  have  abjured,  sworn,  promised,  and  bound  my- 
self, as  above ;  and  in  witness  thereof,  with  my  own 
hand  have  subscribed  this  present  writing  of  my  abjura- 
tion, which  I  have  recited,  word  for  word. 

"  At  Rome,  in  the  Convent  of  Minerva,  twenty-sec- 
ond June,  1633,  I,  Galileo  Galilei,  have  abjured  as 
above,  with  my  own  hand." 

From  the  court  Galileo  was  conducted  to  prison,  to  be 
immured  for  life  in  one  of  the  dungeons  of  the  Inquisi- 
tion. His  sentence  was  afterwards  mitigated,  and  he 
was  permitted  to  return  to  Florence ;  but  the  humilia- 
tion to  which  he  had  been  subjected  pressed  heavily  on 
his  spirits,  beset  as  he  was  with  infirmities,  and  totally 
blind,  and  he  never  more  talked  or  wrote  on  the  subject 
of  astronomy. 

There  was  enough  in  the  character  of  Galileo  to  com- 
mand a  high  admiration.  There  was  much,  also,  in  his 
sufferings  in  the  cause  of  science,  to  excite  the  deepest 
sympathy,  and  even  compassion.  He  is  moreover  uni- 
versally represented  to  have  been  a  man  of  great  equa- 
nimity, and  of  a  noble  and  generous  disposition.  No  sci- 
entific character  of  the  age,  or  perhaps  of  any  age,  forms 
a  structure  of  finer  proportions,  or  wears  in  a  higher  de- 
gree the  grace  of  symmetry.  Still,  we  cannot  approve 
of  his  employing  artifice  in  the  promulgation  of  truth; 
and  we  are  compelled  to  lament  that  his  lofty  spirit  bow- 
ed in  the  final  conflict.  How  far,  therefore,  he  sinks  be- 
low the  dignity  of  the  Christian  martyr  !  "  At  the  age 
of  seventy,"  says  Dr.  Brewster,  in  his  life  of  Sir  Isaac 
Newton,  "  on  his  bended  knees,  and  with  his  right 


274  LETTERS   ON  ASTRONOMY. 

hand  resting  on  the  Holy  Evangelists,  did  this  patriarch 
of  science  avow  his  present  and  past  belief  in  the  dog- 
mas of  the  Romish  Church,  abandon  as  false  and  heret- 
ical the  doctrine  of  the  earth's  motion  and  of  the  sun's 
immobility,  and  pledge  himself  to  denounce  to  the  In- 
quisition any  other  person  who  was  even  suspected  of 
heresy.  He  abjured,  cursed,  and  detested,  those  eter- 
nal and  immutable  truths  which  the  Almighty  had  per- 
mitted him  to  be  the  first  to  establish.  Had  Galileo  but 
added  the  courage  of  the  martyr  to  the  wisdom  of  the 
sage  ;  had  he  carried  the  glance  of  his  indignant  eye 
round  the  circle  of  his  judges ;  had  he  lifted  his  hands 
to  heaven,  and  called  the  living  God  to  witness  the  truth 
and  immutability  of  his  opinions ;  the  bigotry  of  his 
enemies  would  have  been  disarmed,  and  science  would 
have  enjoyed  a  memorable  triumph." 


LETTER  XXIII. 

SATURN. URANUS. ASTEROIDS. 

"  Into  the  Heaven  of  Heavens  I  have  presumed, 
An  earthly  guest,  and  drawn  empyreal  air." — Milton. 

THE  consideration  of  the  system  of  Jupiter  and  his 
satellites  led  us  to  review  the  interesting  history  of  Gal- 
ileo, who  first,  by  means  of  the  telescope,  disclosed  the 
knowledge  of  that  system  to  the  world.  I  will  now 
proceed  with  the  other  superior  planets. 

SATURN,  as  well  as  Jupiter,  has  within  itself  a  system 
on  a  scale  of  great  magnificence.  In  size  it  is  next  to 
Jupiter  the  largest  of  the  planets,  being  seventy-nine 
thousand  miles  in  diameter,  or  about  one  thousand 
times  as  large  as  the  earth.  It  has  likewise  belts  on  its 
surface,  and  is  attended  by  seven  satellites.  But  a  still 
more  wonderful  appendage  is  its  Ring,  a  broad  wheel, 
encompassing  the  planet  at  a  great  distance  from  it. 
As  Saturn  is  nine  hundred  millions  of  miles  from  us, 
we  require  a  more  powerful  telescope  to  see  his  glories, 


SATURN.  275 

in  all  their  magnificence,  than  we  do  to  enjoy  a  full 
view  of  the  system  of  Jupiter.  When  we  are  privi- 
leged with  a  view  of  Saturn,  in  his  most  favorable  po- 
sitions, through  a  telescope  of  the  larger  class,  the. 
mechanism  appears  more  wpnderful  than  even  that  of 
Jupiter. 

Saturn's  ring,  when  viewed  with  telescopes  of  a  high 
power,  is  found  to  consist  of  two  concentred  rings, 
separated  from  each  other  by  a  dark  space.  Although 
this  division  of  the  rings  appears  to  us,  on  account  of 
our  immense  distance,  as  only  a  fine  line,  yet  it  is,  in 
reality,  an  interval  of  not  less  than  eighteen  hundred 
miles.  The  dimensions  of  the  whole  system  are,  in 
round  numbers,  as  follows : 

Miles. 

Diameter  of  the  planet,  .  .  .  .  .  79,000 
From  the  surface  of  the  planet  to  the  inner  ring,  20,000 
Breadth  of  the  inner  ring,  .  .  .  17,000 
Interval  between  the  rings,  ....  1,800 
Breadth  of  the  outer  ring,  .  *  .;  .  10,500 
Extreme  dimensions  from  outside  to  outside,  176,000 

Figure  60,  facing  page  247,  represents  Saturn,  as  it 
appears  to  a  powerful  telescope,  surrounded  by  its  rings, 
and  having  its  body  striped  with  dark  belts,  somewhat 
similar,  but  broader  and  less  strongly  marked  than  those 
of  Jupiter.  In  telescopes  of  inferior  power,  but  still 
sufficient  to  see  the  ring  distinctly,  we  should  scarcely 
discern  the  belts  at  all.  We  might,  however,  observe 
the  shadow  cast  upon  the  ring  by  the  planet,  (as  seen 
in  the  figure  on  the  right,  on  the  upper  side ;)  and,  in 
favorable  situations  of  the  planet,  we  might  discern 
glimpses  of  the  shadow  of  the  ring  on  the  body  of  the 
planet,  on  the  lower  side  beneath  the  ring.  To  see 
the  division  of  the  ring  and  the  satellites  requires  a 
better  telescope  than  is  in  possession  of  most  observers. 
With  smaller  telescopes,  we  may  discover  an  oval  fig- 
ure of  peculiar  appearance,  which  it  would  be  difficult 
to  interpret.  Galileo,  who  first  saw  it  in  the  year  1610, 


276  LETTERS  ON  ASTRONOMY. 

recognised  this  peculiarity,  but  did  not  know  what  it 
meant.  Seeing  something  in  the  centre  with  two  pro- 
jecting arms,  one  on  each  side,  he  concluded  that  the 
planet  was  triple-shaped.  This  was,  at  the  time,  all  he 
could  learn  respecting  it,  as  the  telescopes  he  possessed 
were  very  humble,  compared  with  those  now  used  by 
astronomers.  The  first  constructed  by  him  magnified 
but  three  times  ;  his  second,  eight  times  ;  and  his  best, 
only  thirty  times,  which  is  no  better  than  a  common 
ship-glass. 

It  was  the  practice  of  the  astronomers  of  those  days 
to  give  the  first  intimation  of  a  new  discovery  in  a  Lat- 
in verse,  the  letters  of  which  were  transposed.  This 
would  enable  them  to  claim  priority,  in  case  any  other 
person  should  contest  the  honor  of  the  discovery,  and 
at  the  same  time  would  afford  opportunity  to  complete 
their  observations,  before  they  published  a  full  account 
of  them.  Accordingly,  Galileo  announced  the  discov- 
ery of  the  singular  appearance  of  Saturn  under  this 
disguise,  in  a  line  which,  when  the  transposed  letters 
were  restored  to  their  proper  places,  signified  that  he 
had  observed,  "  that  the  most  distant  planet  is  triple- 
formed."*  He  shortly  afterwards,  at  the  request  of  his 
patron,  the  Emperor  Rodolph,  gave  the  solution,  and 
added,  "  I  have,  with  great  admiration,  observed  that 
Saturn  is  not  a  single  star,  but  three  together,  which, 
as  it  were,  touch  each  other  ;  they  have  no  relative  mo- 
tion, and  are  constituted  of  this  form,  oOo,  the  middle 
one  being  somewhat  larger  than  the  two  lateral  ones. 
If  we  examine  them  with  an  eye-glass  which  magnifies 
the  surface  less  than  one  thousand  times,  the  three  stars 
do  not  appear  very  distinctly,  but  Saturn  has  an  oblong 
appearance,  like  that  of  an  olive,  thus,  o.  Now,  I 
have  discovered  a  court  for  Jupiter,  (alluding  to  his 
satellites,)  and  two  servants  for  this  old  man,  (Saturn,) 
who  aid  his  steps,  and  never  quit  his  side." 

It  was  by  this  mystic  light  that  Galileo  groped  his 

*  Altissimum  planetam  tergeminum  observavi.    Or,  as  transposed, 
Smaismrmilme  poeta  leumi  bvne  nugttaviras. 


SATURN.  277 

way  through  an  organization  which,  under  the  more 
powerful  glasses  of  his  successors,  was  to  expand  into 
a  mighty  orb,  encompassed  by  splendid  rings  of  vast 
dimensions,  the  whole  attended  by  seven  bright  satel- 
lites. This  system  was  first  fully  developed  by  Huy- 
ghens,  a  Dutch  astronomer,  about  forty  years  after- 
wards.* It  requires  a  superior  telescope  to  see  it  to 
advantage ;  but,  when  seen  through  such  a  telescope, 
it  is  one  of  the  most  charming  spectacles  afforded  to 
that  instrument.  To  give  some  idea  of  the  properties 
of  a  telescope  suited  to  such  observations,  I  annex  an 
extract  from  an  account,  that  was  published  a  few  years 
since,  of  a  telescope  constructed  by  Mr.  Tully,  a  distin- 
guished English  artist.  "  The  length  of  the  instrument 
was  twelve  feet,  but  was  easily  adjusted,  and  was  per- 
fectly steady.  The  magnifying  powers  ranged  from 
two  hundred  to  seven  hundred  and  eighty  times ;  but 
the  great  excellence  of  the  telescope  consisted  more  in 
the  superior  distinctness  and  brilliancy  with  which  ob- 
jects were  seen  through  it,  than  in  its  magnifying  pow- 
ers. With  a  power  of  two  hundred  and  forty,  the 
light  of  Jupiter  was  almost  more  than  the  eye  could 
bear,  and  his  satellites  appeared  as  bright  as  Sirius, 
but  with  a  clear  and  steady  light ;  and  the  belts  and 
spots  on  the  face  of  the  planet  were  most  distinctly 
defined.  With  a  power  of  nearly  four  hundred,  Sa- 
turn appeared  large  and  well  defined,  and  was  one  of 
the  most  beautiful  objects  that  can  well  be  conceived." 
That  the  ring  is  a  solid  opaque  substance,  is  shown 
by  its  throwing  its  shadow  on  the  body  of  the  planet 
on  the  side  nearest  the  sun,  and  on  the  other  side  re- 
ceiving that  of  the  body.  The  ring  encompasses  the 
equatorial  regions  of  the  planet,  and  the  planet  revolves 
on  an  axis  which  is  perpendicular  to  the  plane  of  the 

*  In  imitation  of  Galileo,  Huyghens  announced  his  discovery  in 
this  form  raaaaaaacccccdeeeeeghiiiiiiillllmmnn 
nnnnnnnooooppqrrstttttuuuuu;  which  he  afterwards 
recomposed  into  this  sentence  :  JLnnulo  cingitur,  tenui,  piano,  nus- 
quam  coh&re?iie,  ad  eclipticam  inclinato. 

24  L.   A. 


278  LETTERS  ON  ASTRONOMY. 

ring  in  about  ten  and  a  half  hours.  This  is  known  by 
observing  the  rotation  of  certain  dusky  spots,  which 
sometimes  appear  on  its  surface.  This  motion  is  near- 
ly the  same  with  the  diurnal  motion  of  Jupiter,  subject- 
ing places  on  the  equator  of  the  planet  to  a  very  swift 
revolution,  and  occasioning  a  high  degree  of  compres- 
sion at  the  poles,  the  equatorial  being  to  the  polar  di- 
ameter in  the  high  ratio  of  eleven  to  ten. 

Saturn's  ring,  in  its  revolution  around  the  sun,  always 
remains  parallel  to  itself.  If  we  hold  opposite  to  the 
eye  a  circular  ring  or  disk,  like  a  piece  of  coin,  it  will 
appear  as  a  complete  circle  only  when  it  is  at  right  an- 
gles to  the  axis  of  vision.  When  it  is  oblique  to  that 
axis,  it  will  be  projected  into  an  ellipse  more  and  more 
flattened,  as  its  obliquity  is  increased,  until,  when  its 
plane  coincides  with  the  axis  of  vision,  it  is  projected 
into  a  straight  line.  Please  to  take  some  circle,  as  a 
flat  plate,  (whose  rim  may  well  represent  the  ring  of 
Saturn.)  and  hold  it  in  these  different  positions  before 
the  eye.  Now,  place  on  the  table  a  lamp  to  represent 
the  sun,  and  holding  the  ring  at  a  certain  distance,  in- 
clined a  little  towards  the  lamp,  carry  it  round  the 
lamp,  always  keeping  it  parallel  to  itself.  During  its 
revolution,  it  will  twice  present  its  edge  to  the  lamp  at 
opposite  points  ;  and  twice,  at  places  ninety  degrees 
distant  from  those  points,  it  will  present  its  broadest 
face  towards  the  lamp.  At  intermediate  points,  it  will 
exhibit  an  ellipse  more  or  less  open,  according  as  it  is 
nearer  one  or  the  other  of  the  preceding  positions.  It 
will  be  seen,  also,  that  in  one  half  of  the  revolution, 
the  lamp  shines  on  one  side  of  the  ring,  and  in  the 
other  half  of  the  revolution,  on  the  other  side. 

Such  would  be  the  successive  appearances  of  Sa- 
turn's ring  to  a  spectator  on  the  sun  ;  and  since  the  earth 
is,  in  respect  to  so  distant  a  body  as  Saturn,  very  near 
the  sun,  these  appearances  are  presented  to  us  nearly 
in  the  same  manner  as  though  we  viewed  them  from 
the  sun.  Accordingly,  we  sometimes  see  Saturn's  ring 
under  the  form  of  a  broad  ellipse,  which  grows  contin- 


SA.TURN.  279 

ually  more  and  more  acute,  until  it  passes  into  a  line, 
and  we  either  lose  sight  of  it,  altogether,  or,  by  the  aid 
of  the  most  powerful  telescopes,  we  see  it  as  a  fine 
thread  of  light  drawn  across  the  disk,  and  projecting 
out  from  it  on  each  side.  As  the  whole  revolution  oc- 
cupies thirty  years,  and  the  edge  is  presented  to  the 
sun  twice  in  the  revolution,  this  last  phenomenon, 
namely,  the  disappearance  of  the  ring,  takes  place  every 
fifteen  years. 

You  may  perhaps  gain  a  still  clearer  idea  of  the  fore- 
going appearances  from  the  following  diagram,  Fig.  61. 

Fig.  61. 


Let  A,  B,  C,  &c.,  represent  successive  positions  of  Sa- 
turn and  his  ring,  in  different  parts  of  his  orbit,  while 
a  b  represents  the  orbit  of  the  earth.  Please  to  re- 
mark, that  these  orbits  are  drawn  so  elliptical,  not  to 
represent  the  eccentricity  of  either  the  earth's  or  Sa- 
turn's orbit,  but  merely  as  the  projection  of  circles  seen 
very  obliquely.  Also,  imagine  one  half  of  the  body  of 
the  planet  and  of  the  ring  to  be  above  the  plane  of  the 
paper,  and  the  other  half  below  it.  Were  the  ring, 
when  at  C  and  G,  perpendicular  to  C  G,  it  would  be 
seen  by  a  spectator  situated  at  a  or  b  as  a  perfect  cir- 
cle ;  but  being  inclined  to  the  line  of  vision  twenty- 
eight  degrees  four  minutes,  it  is  projected  into  an  ellipse. 
This  ellipse  contracts  in  breadth  as  the  ring  passes 
towards  its  nodes  at  A  and  E,  where  it  dwindles  into 
a  straight  line.  From  E  to  G  the  ring  opens  again, 


280  LETTERS  ON  ASTRONOMY. 

becomes  broadest  at  G,  and  again  contracts,  till  it  be- 
comes a  straight  line  at  A,  and  from  this  point  expands, 
till  it  recovers  its  original  breadth  at  C.  These  succes- 
sive appearances  are  all  exhibited  to  a  telescope  of 
moderate  powers. 

The  ring  is  extremely  thin,  since  the  smallest  satel- 
lite, when  projected  on  it,  more  than  covers  it.  The 
thickness  is  estimated  at  only  one  hundred  miles.  Sa- 
turn's ring  shines  wholly  by  reflected  light  derived  from 
the  sun.  This  is  evident  from  the  fact  that  that  side 
only  which  is  turned  towards  the  sun  is  enlightened ; 
and  it  is  remarkable,  that  the  illumination  of  the  ring 
is  greater  than  that  of  the  planet  itself,  but  the  outer 
ring  is  less  bright  than  the  inner.  Although  we  view 
Saturn's  ring  nearly  as  though  we  saw  it  from  the  sun, 
yet  the  plane  of  the  ring  produced  may  pass  between 
the  earth  and  the  sun,  in  which  case,  also,  the  ring  be- 
comes invisible,  the  illuminated  side  being  wholly  turned 
from  us.  Thus,  when  the  ring  is  approaching  its  node 
at  E,  a  spectator  at  a  would  have  the  dark  side  of  the 
ring  presented  to  him.  The  ring  was  invisible  in  1833, 
and  will  be  invisible  again  in  1847.  The  northern  side 
of  the  ring  will  be  in  sight  until  1855,  when  the  south- 
ern side  will  come  into  view.  It  appears,  therefore, 
that  there  are  three  causes  for  the  disappearance  of 
Saturn's  ring :  first,  when  the  edge  of  the  ring  is  pre- 
sented to  the  sun  ;  secondly,  when  -the  edge  is  present- 
ed to  the  earth ;  and  thirdly,  when  the  unilluminated 
side  is  towards  the  earth. 

Saturn's  ring  revolves  in  its  own  plane  in  about  ten 
ind  a  half  hours.  La  Place  inferred  this  from  the  doc- 
trine of  universal  gravitation.  He  proved  that  such  a 
rotation  was  necessary  ;  otherwise,  the  matter  of  which 
the  ring  is  composed  would  be  precipitated  upon  its 
primary.  He  showed  that,  in  order  to  sustain  itself,  its 
period  of  rotation  must  be  equal  to  the  time  of  revolu- 
tion of  a  satellite,  circulating  around  Saturn  at  a  dis- 
tance from  it  equal  to  that  of  the  middle  of  the  ring, 
which  period  would  be  about  ten  and  a  half  hours.  By 


SATURN.  281 

means  of  spots  in  the  ring,  Dr.  Herschel  followed  the 
ring  in  its  rotation,  and  actually  found  its  period  to  be 
the  same  as  assigned  by  La  Place, — a  coincidence 
which  beautifully  exemplifies  the  harmony  of  truth. 

Although  the  rings  have  very  nearly  the  same  centre 
with  the  planet  itself,  yet  recent  measurements  of  ex- 
treme delicacy  have  demonstrated,  that  the  coincidence 
is  not  mathematically  exact,  but  that  the  centre  of 
gravity  of  the  rings  describes  around  that  of  the  body 
a  very  minute  orbit.  "  This  fact,"  says  Sir  J.  Her- 
schel, "  unimportant  as  it  may  seem,  is  of  the  utmost 
consequence  to  the  stability  of  the  system  of  rings. 
Supposing  them  mathematically  perfect  in  their  circular 
form,  and  exactly  concentric  with  the  planet,  it  is  de- 
monstrable that  they  would  form  (in  spite  of  their  cen- 
trifugal force)  a  system  in  a  state  of  unstable  equilib- 
rium, which  the  slightest  external  power  would  subvert, 
not  by  causing  a  rupture  in  the  substance  of  the  rings, 
but  by  precipitating  them  unbroken  upon  the  surface 
of  the  planet."  The  ring  may  be  supposed  of  an  un- 
equal breadth  in  its  different  parts,  and  as  consisting 
of  irregular  solids,  whose  common  centre  of  gravity 
does  not  coincide  with  the  centre  of  the  figure.  Were 
it  not  for  this  distribution  of  matter,  its  equilibrium 
would  be  destroyed  by  the  slightest  force,  such  as  the 
attraction  of  a  satellite,  and  the  ring  would  finally  pre- 
cipitate itself  upon  the  planet.  Sir  J.  Herschel  further 
observes,  that,  uas  the  smallest  difference  of  velocity 
between  the  planet  and  its  rings  must  infallibly  precip- 
itate the  rings  upon  the  planet,  never  more  to  separate, 
it  follows,  either  that  their  motions  in  their  common 
orbit  round  the  sun  must  have  been  adjusted  to  each 
other  by  an  external  power,  with  the  minutest  precision, 
or  that  the  rings  must  have  been  formed  about  the 
planet  while  subject  to  their  common  orbitual  motion, 
and  under  the  full  and  free  influence  of  all  the  acting 
forces. 

"The  rings  of  Saturn  must  present  a  magnificent 
spectacle  from  those  regions  of  the  planet  which  lie  on 
24* 


282  LETTERS  ON  ASTRONOMY. 

their  enlightened  sides,  appearing  as  vast  arches  span- 
ning the  sky  from  horizon  to  horizon,  and  holding  an 
invariable  situation  among  the  stars.  On  the  other 
hand,  in  the  region  beneath  the  dark  side,  a  solar 
eclipse  of  fifteen  years  in  duration,  under  their  shadow, 
must  afford  (to  our  ideas)  an  inhospitable  abode  to  an- 
imated beings,  but  ill  compensated  by  the  full  light  of 
its  satellites.  But  we  shall  do  wrong  to  judge  of  the 
fitness  or  unfitness  of  their  condition,  from  what  we 
see  around  us,  when,  perhaps,  the  very  combinations 
which  convey  to  our  minds  only  images  of  horror,  may 
be  in  reality  theatres  of  the  most  striking  and  glorious 
displays  of  beneficent  contrivance." 

Saturn  is  attended  by  seven  satellites.  Although 
they  are  bodies  of  considerable  size,  their  great  distance 
prevents  their  being  visible  to  any  telescope  but  such 
as  afford  a  strong  light  and  high  magnifying  powers. 
The  outermost  satellite  is  distant  from  the  planet  more 
than  thirty  times  the  planet's  diameter,  and  is  by  far 
the  largest  of  the  whole.  It  exhibits,  like  the  satellites 
of  Jupiter,  periodic  variations  of  light,  which  prove  its 
revolution  on  its  axis  in  the  time  of  a  sidereal  revolu- 
tion about  Saturn,  as  is  the  case  with  our  moon,  while 
performing  its  circuit  about  the  earth.  The  next  sat- 
ellite in  order,  proceeding  inwards,  is  tolerably  con- 
spicuous ;  the  three  next  are  very  minute,  and  require 
powerful  telescopes  to  see  them ;  while  the  two  interior 
satellites,  which  just  skirt  the  edge  of  the  ring,  and 
move  exactly  in  its  plane,  have  never  been  discovered 
but  with  the  most  powerful  telescopes  which  human 
art  has  yet  constructed,  and  then  only  under  peculiar 
circumstances.  At  the  time  of  the  disappearance  of 
the  rings,  (to  ordinary  telescopes.)  they  were  seen  by 
Sir  William  Herschel,  with  his  great  telescope,  pro- 
jected along  the  edge  of  the  ring,  and  threading,  like 
beads,  the  thin  fibre  of  light  to  which  the  ring  is  then 
reduced.  Owing  to  the  obliquity  of  the  ring,  and  of 
the  orbits  of  the  satellites,  to  that  of  their  primary, 
there  are  no  eclipses  of  the  satellites,  the  two  interior 


URANUS.  283 

ones  excepted,  until  near  the  time  when  the  ring  is 
seen  edgewise. 

"  The  firmament  of  Saturn  will  unquestionably  pre- 
sent to  view  a  more  magnificent  and  diversified  scene 
of  celestial  phenomena  than  that  of  any  other  planet 
in  our  system.  It  is  placed  nearly  in  the  middle  of 
that  space  which  intervenes  between  the  sun  and  the 
orbit  of  the  remotest  planet.  Including  its  rings  and 
satellites,  it  may  be  considered  as  the  largest  body  or 
system  of  bodies  within  the  limits  of  the  solar  system ; 
and  it  excels  them  all  in  the  sublime  and  diversified 
apparatus  with  which  it  is  accompanied.  In  these  re- 
spects, Saturn  may  justly  be  considered  as  the  sove- 
reign among  the  planetary  hosts.  The  prominent  parts 
of  its  celestial  scenery  may  be  considered  as  belonging 
to  its  own  system  of  rings  and  satellites,  and  the  views 
which  will  occasionally  be  opened  of  the  firmament  of 
the  fixed  stars ;  for  few  of  the  other  planets  will  make 
their  appearance  in  its  sky.  Jupiter  will  appear  alter- 
nately as  a  morning  and  an  evening  star,  with  about  the 
same  degree  of  brilliancy  it  exhibits  to  us ;  but  it  will 
seldom  be  conspicuous,  except  near  the  period  of  its 
greatest  elongation  ;  and  it  will  never  appear  to  remove 
from  the  sun  further  than  thirty-seven  degrees,  and  con- 
sequently will  not  appear  so  conspicuous,  nor  for  such 
a  length  of  time,  as  Venus  does  to  us.  Uranus  is  the 
only  other  planet  which  will  be  seen  from  Saturn,  and 
it  will  there  be  distinctly  perceptible,  like  a  star  of  the 
third  magnitude,  when  near  the  time  of  its  opposition 
to  the  sun.  But  near  the  time  of  its  conjunction  it 
will  be  completely  invisible,  being  then  eighteen  hun- 
dred millions  of  miles  more  distant  than  at  the  opposi- 
tion, and  eight  hundred  millions  of  miles  more  distant 
from  Saturn  than  it  ever  is  from  the  earth  at  any  pe- 
riod."* 

URANUS. — Uranus  is  the  remotest  planet  belonging 
to  our  system,  and  is  rarely  visible,  except  to  the  tele- 
scope. Although  his  diameter  is  more  than  four  times 
*  Dick's  «  Celestial  Scenery.* 


284  LETTERS  ON  ASTRONOMY. 

that  of  the  earth,  being  thirty-five  thousand  one  hun- 
dred and  twelve  miles,  yet  his  distance  from  the  sun  is 
likewise  nineteen  times  as  great  as  the  earth's  distance, 
or  about  eighteen  hundred  millions  of  miles.  His 
revolution  around  the  sun  occupies  nearly  eighty-four 
years,  so  that  his  position  in  the  heavens,  for  several 
years  in  succession,  is  nearly  stationary.  His  path  lies 
very  nearly  in  the  ecliptic,  being  inclined  to  it  less  than 
one  degree.  The  sun  himself,  when  seen  from  Uranus 
dwindles  almost  to  a  star,  subtending,  as  it  does,  an 
angle  of  only  one  degree  and  forty  minutes ;  so  that 
the  surface  of  the  sun  would  appear  there  four  hundred 
times  less  than  it  it  does  to  us.  This  planet  was  dis- 
covered by  Sir  William  Herschel  on  the  thirteenth  of 
March,  1781.  His  attention  was  attracted  to  it  by  the 
largeness  of  its  disk  in  the  telescope ;  and  finding  that 
it  shifted  its  place  among  the  stars,  he  at  first  took  it  for 
a  comet,  but  soon  perceived  that  its  orbit  was  not  eccen- 
tric, like  the  orbits  of  comets,  but  nearly  circular,  like 
those  of  the  planets.  It  was  then  recognised  as  a  new 
member  of  the  planetary  system,  a  conclusion  which 
has  been  justified  by  all  succeeding  observations.  It 
was  named  by  the  discoverer  the  George  Star,  (Geor- 
gium  Sidus,)  after  his  munificent  patron,  George  the 
Third ;  in  the  United  States,  and  in  some  other  coun- 
tries, it  was  called  Herschel ;  but  the  name  Uranus, 
from  a  Greek  word,  (OVQUVOC,  Ouranos,}  signifying  the 
oldest  of  the  gods,  has  finally  prevailed.  So  distant  is 
Uranus  from  the  sun,  that  light  itself,  which  moves 
nearly  twelve  millions  of  miles  every  minute,  would  re- 
quire more  than  two  hours  and  a  half  to  pass  to  it  from 
the  sun. 

And  now,  having  contemplated  all  the  planets  sep- 
arately, just  cast  your  eyes  on  the  diagram  facing  page 
236,  Fig.  53,  and  you  will  see  a  comparative  view  of 
the  various  magnitudes  of  the  sun,  as  seen  from  each 
of  the  planets. 

Uranus  is  attended  by  six  satellites.  So  minute 
objects  are  they,  that  they  can  be  seen  only  by  power- 


URANUS.  285 

ful  telescopes.  Indeed,  the  existence  of  more  than  two 
is  still  considered  as  somewhat  doubtful.  These  two, 
however,  offer  remarkable  and  indeed  quite  unexpect- 
ed and  unexampled  peculiarities.  Contrary  to  the 
unbroken  analogy  of  the  whole  planetary  system,  the 
planes  of  their  orbits  are  nearly  perpendicular  to  the 
ecliptic,  and  in  these  orbits  their  motions  are  retrograde ; 
that  is,  instead  of  advancing  from  west  to  east  around 
their  primary,  as  is  the  case  with  all  the  other  planets 
and  satellites,  they  move  in  the  opposite  direction. 
With  this  exception,  all  the  motions  of  the  planets, 
whether  around  their  own  axes,  or  around  the  sun,  are 
from  west  to  east.  The  sun  himself  turns  on  his  axis 
from  west  to  east ;  all  the  primary  planets  revolve 
around  the  sun  from  west  to  east ;  their  revolutions  on 
their  own  axes  are  also  in  the  same  direction ;  all  the 
secondaries,  with  the  single  exception  above  mentioned, 
move  about  their  primaries  from  west  to  east;  and, 
finally,  such  of  the  secondaries  as  have  been  discovered 
to  have  a  diurnal  revolution,  follow  the  same  course. 
Such  uniformity  among  so  many  motions  could  have 
resulted  only  from  forces  impressed  upon  them  by  the 
same  Omnipotent  hand  ;  and  few  things  in  the  creation 
more  distinctly  proclaim  that  God  made  the  world. 

Retiring  now  to  this  furthest  verge  of  the  solar  sys- 
tem, let  us  for  a  moment  glance  at  the  aspect  of  the 
firmament  by  night.  Notwithstanding  we  have  taken 
a  flight  of  eighteen  hundred  millions  of  miles,  the  same 
starry  canopy  bends  over  our  heads ;  Sirius  still  shines 
with  exactly  the  same  splendor  as  here ;  Orion,  the 
Scorpion,  the  Great  and  the  Little  Bear,  all  occupy  the 
same  stations ;  and  the  Galaxy  spans  the  sky  with  the 
same  soft  and  mysterious  light.  The  planets,  however, 
with  the  exception  of  Saturn,  are  all  lost  to  the  view, 
being  too  near  the  sun  ever  to  be  seen ;  and  Saturn 
himself  is  visible  only  at  distant  intervals,  at  periods  of 
fifteen  years,  when  at  its  greatest  elongations  from  the 
sun,  and  is  then  too  near  the  sun  to  permit  a  clear  view 
of  his  rings,  much  less  of  the  satellites  that  unite  with 


286  LETTERS  ON  ASTRONOMY. 

the  rings  to  compose  his  gorgeous  retinue.  Comets, 
moving  slowly  as  they  do  when  •so  distant  from  the  sun, 
will  linger  much  longer  in  the  firmament  of  Uranus 
than  in  ours. 

Although  the  sun  sheds  by  day  a  dim  and  cheerless 
light,  yet  the  six  satellites  that  enlighten  and  diversify 
the  nocturnal  sky  present  interesting  aspects.  "  Let 
us  suppose  one  satellite  presenting  a  surface  in  the  sky 
eight  or  ten  times  larger  than  our  moon  ;  a  second,  five 
or  six  times  larger ;  a  third,  three  times  larger ;  a  fourth, 
twice  as  large ;  a  fifth,  about  the  same  size  as  the 
moon  ;  a  sixth,  somewhat  smaller ;  and,  perhaps,  three 
or  four  others  of  different  apparent  dimensions :  let  us 
suppose  two  or  three  of  those,  of  different  phases, 
moving  along  the  concave  of  the  sky,  at  one  period 
four  or  five  of  them  dispersed  through  the  heavens,  one 
rising  above  the  horizon,  one  setting,  one  on  the  merid- 
ian, one  towards  the  north,  and  another  towards  the 
south  ;  at  another  period,  five  or  six  of  them  displaying 
their  lustre  in  the  form  of  a  half  moon,  or  a  crescent, 
in  one  quarter  of  the  heavens ;  and,  at  another  time, 
the  whole  of  these  moons  shining,  with  full  enlightened 
hemispheres,  in  one  glorious  assemblage,  and  we  shall 
have  a  faint  idea  of  the  beauty,  variety,  and  sublimity 
of  the  firmament  of  Uranus."* 

The  New  Planets, — Ceres,  Pallas,  Juno,  and  Vesta. 
— The  commencement  of  the  present  century  was  ren- 
dered memorable  in  the  annals  of  astronomy,  by  the 
discovery  of  four  new  planets,  occupying  the  long  va- 
cant tract  between  Mars  and  Jupiter.  Kepler,  from 
some  analogy  which  he  found  to  subsist  among  the  dis- 
tances of  the  planets  from  the  sun,  had  long  before 
suspected  the  existence  of  one  at  this  distance  ;  and 
his  conjecture  was  rendered  more  probable  by  the  dis- 
covery of  Uranus,  which  follows  the  analogy  of  the  other 
planets.  So  strongly,  indeed,  were  astronomers  im- 
pressed with  the  idea  that  a  planet  would  be  found  be- 
tween Mars  and  Jupiter,  that,  in  the  hope  of  discovering 
*  Pick's  '  Celestial  Scenery,' 


CERES,  PALLAS,  JUNO,  AND  VESTA.  287 

it,  an  association  was  formed  on  the  continent  of  Eu- 
rope, of  twenty-four  observers,  who  divided  the  sky 
into  as  many  zones,  one  of  which  was  allotted  to  each 
member  of  the  association.  The  discovery  of  the  first 
of  these  bodies  was,  however,  made  accidentally  by 
Piazzi,  an  astronomer  of  Palermo,  on  the  first  of  Janu- 
ary, 1801.  It  was  shortly  afterwards  lost  sight  of  on 
account  of  its  proximity  to  the  sun,  and  was  not  seen 
again  until  the  close  of  the  year,  when  it  was  re-dis- 
covered in  Germany.  Piazzi  called  it  Ceres,  in  honor 
of  the  tutelary  goddess  of  Sicily,  and  her  emblem,  the 
sickle,  (9)  has  been  adopted  as  its  appropriate  symbol. 

The  difficulty  of  finding  Ceres  induced  Dr.  Olbers, 
of  Bremen,  to  examine  with  particular  care  all  the  small 
stars  that  lie  near  her  path,  as  seen  from  the  earth  ;  and, 
while  prosecuting  these  observations,  in  March,  1802, 
he  discovered  another  similar  body,  very  nearly  at  the 
same  distance  from  the  sun,  and  resembling  the  former 
in  many  other  particulars.  The  discoverer  gave  to  this 
second  planet  the  name  of  Pallas,  choosing  for  its  sym- 
bol the  lance,  ($)  the  characteristic  of  Minerva. 

The  most  surprising  circumstance  connected  with 
the  discovery  of  Pallas  was  the  existence  of  two  plan- 
ets at  nearly  the  same  distance  from  the  sun,  and  ap- 
parently crossing  the  ecliptic  in  the  same  part  of  the 
heavens,  or  having  the  same  node.  On  account  of  this 
singularity,  Dr.  Olbers  was  led  to  conjecture  that  Ceres 
and  Pallas  are  only  fragments  of  a  larger  planet,  which 
had  formerly  circulated  at  the  same  distance,  and  been 
shattered  by  some  internal  convulsion.  The  hypothe- 
sis suggested  the  probability  that  there  might  be  other 
fragments,  whose  orbits  might  be  expected  to  cross 
the  ecliptic  at  a  common  point,  or  to  have  the  same 
node.  Dr.  Olbers,  therefore,  proposed  to  examine 
carefully,  every  month,  the  two  opposite  parts  of  the 
heavens  in  which  the  orbits  of  Ceres  and  Pallas  in- 
tersect one  another,  with  a  view  to  the  discovery  of 
other  planets,  which  might  be  sought  for  in  those  parts 
with  a  greater  chance  of  success,  than  in  a  wider  zone, 


288  LETTERS   ON  ASTRONOMY. 

embracing  the  entire  limits  of  these  orbits.  According- 
ly, in  1804,  near  one  of  the  nodes  of  Ceres  and  Pallas, 
a  third  planet  was  discovered.  This  was  called  Juno, 
and  the  character  (<J>)  was  adopted  for  its  symbol, 
representing  the  starry  sceptre  of  the  Queen  of  Olym- 
pus. Pursuing  the  same  researches,  in  1807  a  fourth 
planet  was  discovered,  to  which  was  given  the  name 
of  Vesta,  and  for  its  symbol  the  character  (f[)  was 
chosen, — an  altar  surmounted  with  a  censer  holding 
the  sacred  fire. 

The  average  distance  of  these  bodies  from  the  sun 
is  two  hundred  and  sixty-one  millions  of  miles ;  and  it 
is  remarkable  that  their  orbits  are  very  near  together. 
Taking  the  distance  of  the  earth  from  the  sun  for  uni- 
ty, their  respective  distances  are  2.77,  2.77,  2.67,  2.37. 
Their  times  of  revolution  around  the  sun  are  nearly 
equal,  averaging  about  four  and  a  half  years. 

In  respect  to  the  inclination  of  their  orbits  to  the 
ecliptic,  there  is  also  considerable  diversity.  The  orbit 
of  Vesta  is  inclined  only  about  seven  degrees,  while 
that  of  Pallas  is  more  than  thirty-four  degrees.  They 
all,  therefore,  have  a  higher  inclination  than  the  orbits 
of  the  old  planets,  and  of  course  make  excursions  from 
the  ecliptic  beyond  the  limits  of  the  zodiac.  Hence 
they  have  been  called  the  ultra-zodiacal  planets. 
When  first  discovered,  before  their  place  in  the  system 
was  fully  ascertained  it  was  also  proposed  to  call  them 
asteroids,  a  name  implying  that  they  were  planets  un- 
der the  form  of  stars.  Their  title,  however,  to  take 
their  rank  among  the  primary  planets,  is  now  generally 
conceded. 

The  eccentricity  of  their  orbits  is  also,  in  general, 
greater  than  that  of  the  old  planets.  You  will  recol- 
lect that  this  language  denotes  that  their  orbits  are 
more  elliptical,  or  depart  further  from  the  circular  form. 
The  eccentricities  of  the  orbits  of  Pallas  and  Juno  ex- 
ceed that  of  the  orbit  of  Mercury.  The  asteroids 
differ  so  much,  however,  in  eccentricity,  that  their  or- 
bits may  cross  each  other.  The  orbits  of  the  old  plan- 


CERES,  PALLAS,  JUNO,  AND  VESTA.  289 

ets  are  so  nearly  circular,  and  at  such  a  great  distance 
apart,  that  there  is  no  danger  of  their  interfering  with 
each  other.  The  earth,  for  example,  when  at  its  nearest 
distance  from  the  sun,  will  never  come  so  near  it  as 
Venus  is  when  at  its  greatest  distance,  and  therefore 
can  never  cross  the  orbit  of  Venus.  But  since  the  av- 
erage distance  of  Ceres  and  Pallas  from  the  sun  is  about 
the  same,  while  the  eccentricity  of  the  orbit  of  Pallas 
is  much  greater  than  that  of  Ceres,  consequently,  Pal- 
las may  come  so  near  to  the  sun  at  its  perihelion,  as  to 
cross  the  orbit  of  Ceres. 

The  small  size  of  the  asteroids  constitutes  one  of 
their  most  remarkable  peculiarities.  The  difficulty  of 
estimating  the  apparent  diameter  of  bodies  at  once  so 
very  small  and  so  far  off,  would  lead  us  to  expect  dif- 
ferent results  in  the  actual  estimates.  Accordingly, 
while  Dr.  Herschel  estimates  the  diameter  of  Pallas  at 
only  eighty  miles,  Schroeter  places  it  as  high  as  two 
thousand  miles,  or  about  the  diameter  of  the  moon. 
The  volume  of  Vesta  is  estimated  at  only  one  fifteen 
thousandth  part  of  the  earth's,  and  her  surface  is  only 
about  equal  to  that  of  the  kingdom  of  Spain. 

These  little  bodies  are  surrounded  by  atmospheres 
of  great  extent,  some  of  which  are  uncommonly  lumi- 
nous, and  others  appear  to  consist  of  nebulous  matter, 
like  that  of  comets.  These  planets  shine  with  a  more 
vivid  light  than  might  be  expected,  from  their  great  dis- 
tance and  diminutive  size  ;  but  a  good  telescope  is  es- 
sential for  obtaining  a  distinct  view  of  their  phenomena. 

Although  the  great  chasm  which  occurs  between 
Mars  and  Jupiter, — a  chasm  of  more  than  three  hun- 
dred millions  of  miles, — suggested  long  ago  the  idea 
of  other  planetary  bodies  occupying  that  part  of  the 
solar  system,  yet  the  discovery  of  the  asteroids  does 
not  entirely  satisfy  expectation  since  they  are  bodies 
so  dissimilar  to  the  other  members  of  the  series  in  size, 
in  appearance,  and  in  the  form  and  inclinations  of  their 
orbits.  Hence,  Dr.  Olbers,  the  discoverer  of  three  of 
these  bodies,  held  that  they  were  fragments  of  a  single 

25  L.  A. 


290  LETTERS  ON  ASTRONOMi'. 

large  planet,  which  once  occupied  that  place  in  the 
system,  and  which  exploded  in  different  directions  by 
some  internal  violence.  Of  the  fragments  thus  projec- 
ted into  space,  some  would  be  propelled  in  such  direc- 
tions and  with  such  velocities,  as,  under  the  force  of 
projection  and  that  of  the  solar  attraction,  would  make 
them  revolve  in  regular  orbits  around  the  sun.  Others 
would  be  so  projected  among  the  other  bodies  in  the 
system,  as  to  be  thrown  in  very  irregular  orbits,  appar- 
ently wandering  lawless  through  the  skies.  The  larger 
fragments  would  receive  the  least  impetus  from  the  ex- 
plosive force,  and  would  therefore  circulate  in  an  orbit 
deviating  less  than  any  other  of  the  fragments  from  the 
original  path  of  the  large  planet ;  while  the  lesser  frag- 
ments, being  thrown  off  with  greater  velocity,  would  re- 
volve in  orbits  more  eccentric,  and  more  inclined  to  the 
ecliptic. 

Dr.  Brewster,  editor  of  the  '  Edinburgh  Encyclope- 
dia,' and  the  well-known  author  of  various  philosophical 
works,  espoused  this  hypothesis  with  much  zeal ;  and, 
after  summing  up  the  evidence  in  favor  of  it,  he  re- 
marks as  follows  :  "  These  singular  resemblances  in 
the  motions  of  the  greater  fragments,  and  in  those  of 
the  lesser  fragments,  and  the  striking  coincidences  be- 
tween theory  and  observation  in  the  eccentricity  of  their 
orbits,  in  their  inclination  to  the  ecliptic,  in  the  position 
of  their  nodes,  and  in  the  places  of  their  perihelia,  are 
phenomena  which  could  not  possibly  result  from  chance, 
and  which  concur  to  prove,  with  an  evidence  amount- 
ing almost  to  demonstration,  that  the  four  new  planets 
have  diverged  from  one  common  node,  and  have  there- 
fore composed  a  single  planet." 

The  same  distinguished  writer  supposes  that  some 
of  the  smallest  fragments  might  even  have  come  within 
reach  of  the  earth's  attraction,  and  by  the  combined  ef- 
fects of  their  projectile  forces  and  the  attraction  of  the 
earth,  be  made  to  revolve  around  this  body  as  the  lar- 
ger fragments  are  carried  around  the  sun ;  and  that 
these  are  in  fact  the  bodies  which  afford  those  meteoric 


PLANETARY  MOTIONS.  291 

stones  which  are  occasionally  precipitated  to  the  earth. 
It  is  now  a  well-ascertained  fact,  a  fact  which  has  been 
many  times  verified  in  our  own  country,  that  large  mete- 
ors, in  the  shape  of  fire-balls,  traversing  the  atmosphere, 
sometimes  project  to  the  earth  masses  of  stony  or  ferru- 
ginous matter.  Such  were  the  meteoric  stones  which 
fell  at  Weston,  in  Connecticut,  in  1807,  of  which  a  full 
and  interesting  account  was  published,  after  a  minute 
examination  of  the  facts,  by  Professors  Silliman  and 
Kingsley,  of  Yale  College.  Various  accounts  of  sim~ 
ilar  occurrences  may  be  found  in  different  volumes  of 
the  American  Journal  of  Science.  It  is  for  the  pro- 
duction of  these  wonderful  phenomena  that  Dr.  Brews- 
ter  supposes  the  explosion  of  the  planet,  which,  accord- 
ing to  Dr.  Olbers,  produced  the  asteroids,  accounts. 
Others,  however,  as  Sir  John  Herschel,  have  been  dis- 
posed to  ascribe  very  little  weight  to  the  doctrine  of 
Olbers. 


LETTER  XXIV. 

THE  PLANETARY  MOTIONS. KEPLER's  LAWS. KEPLER. 

"  God  of  the  rolling  orbs  above  ! 
Thy  name  is  written  clearly  bright 
In  the  warm  day's  unvarying  blaze, 
Or  evening's  golden  shower  of  light  ^ 
For  every  fire  that  fronts  the  sun, 
And  every  spark  that  walks  alone 
Around  the  utmost  verge  of  heaven, 
Was  kindled  at  thy  burning  throne." — Peabody. 

IF  we  could  stand  upon  the  sun  and  view  the  plan- 
etary motions,  they  would  appear  to  us  as  simple  as  the 
motions  of  equestrians  riding  with  different  degrees  of 
speed  around  a  large  ring,  of  which  we  occupied  the 
centre.  We  should  see  all  the  planets  coursing  each 
other  from  west  to  east,  through  the  same  great  high- 
way, (the  Zodiac,)  no  one  of  them,  with  the  exception 
of  the  asteroids,  deviating  more  than  seven  degrees 
from  the  path  pursued  by  the  earth.  Most  of  them,  in- 


292  LETTERS  ON  ASTRONOMY. 

deed,  would  always  be  seen  moving  much  nearer  than 
that  to  the  ecliptic.  We  should  see  the  planets  mov- 
ing on  their  way  with  various  degrees  of  speed.  Mer- 
cury would  make  the  entire  circuit  in  about  three 
months,  hurrying  on  his  course  with  a  speed  about  one 
third  as  great  as  that  by  which  the  moon  revolves 
around  the  earth.  The  most  distant  planets,  on  the 
other  hand,  move  at  so  slow  a  pace,  that  we  should  see 
Mercury,  Venus,  the  Earth,  and  Mars,  severally  overtak- 
ing them  a  great  many  times,  before  they  had  com- 
pleted their  revolutions.  But  though  the  movements  of 
some  were  comparatively  rapid,  and  of  others  extremely 
slow,  yet  they  would  not  seem  to  differ  materially,  in 
other  respects :  each  would  be  making  a  steady  and 
nearly  uniform  march  along  the  celestial  vault. 

Such  would  be  the  simple  and  harmonious  motions 
of  the  planets,  as  they  would  be  seen  from  the  sun,  the 
centre  of  their  motions  ;  and  such  they  are,  in  fact.  But 
two  circumstances  conspire  to  make  them  appear  ex- 
ceedingly different  from  these,  and  vastly  more  compli- 
cated ;  one  is,  that  we  view  them  uut  of  the  centre  or 
their  motions ;  the  other,  that  we  are  ourselves  in  mo- 
tion. I  have  already  explained  to  you  the  effect  which 
these  two  causes  produce  on  the  apparent  motions  of 
the  inferior  planets,  Mercury  and  Venus.  Let  us  now 
see  how  they  effect  those  of  the  superior  planets,  Mars, 
Jupiter,  Saturn,  and  Uranus. 

Orreries,  or  machines  intended  to  exhibit  a  model 
of  the  solar  system,  are  sometimes  employed  to  give  a 
popular  view  of  the  planetary  motions  ;  but  they  oftener 
mislead  than  give  correct  ideas.  They  may  assist  re- 
flection, but  they  can  never  supply  its  place.  The  im- 
possibility of  representing  things  in  their  just  propor- 
tions will  be  evident,  when  we  reflect  that,  to  do  this, 
if  in  an  orrery  we  make  Mercury  as  large  as  a  cherry, 
we  should  have  to  represent  the  sun  six  feet  in  diam- 
eter. If  we  preserve  the  same  proportions,  in  regard  to 
distance,  we  must  place  Mercury  two  hundred  and  fif- 
ty feet,  and  Uranus  twelve  thousand  five  hundred  feet, 


PLANETARY  MOTIONS.  293 

or  more  than  two  miles  from  the  sun.  The  mind  of 
the  student  of  astronomy  must,  therefore,  raise  itself  from 
such  imperfect  representations  of  celestial  phenomena, 
as  are  afforded  by  artificial  mechanism,  and,  transferring 
his  contemplations  to  the  celestial  regions  themselves, 
he  must  conceive  of  the  sun  and  planets  as  bodies  that 
bear  an  insignificant  ratio  to  the  immense  spaces  in 
which  they  circulate,  resembling  more  a  few  little  birds 
flying  in  the  open  sky,  than  they  do  the  crowded  ma- 
chinery of  an  orrery. 

The  real  motions  of  the  planets,  indeed,  or  such  as 
orreries  usually  exhibit,  are  very  easily  conceived  of,  as 
before  explained ;  but  the  apparent  motions  are,  for 
the  most  part,  entirely  different  from  these.  The  ap- 
parent motions  of  the  inferior  planets  have  been  already 
explained.  You  will  recollect  that  Mercury  and  Ve- 
nus move  backwards  and  forwards  across  the  sun,  the 
former  never  being  seen  further  than  twenty-nine  de- 
grees, and  the  latter  never  more  than  about  forty-seven 
degrees,  from  that  luminary ;  that,  while  passing  from 
the  greatest  elongation  on  one  side,  to  the  greatest  elon- 
gation on  the  other  side,  through  the  superior  conjunc- 
tion, the  apparent  motions  of  these  planets  are  acceler- 
ated by  the  motion  of  the  earth ;  but  that,  while  mov- 
ing through  the  inferior  conjunction,  at  which  time  their 
motions  are  retrograde,  they  are  apparently  retarded 
by  the  earth's  motion.  Let  us  now  see  what  are  the 
apparent  motions  of  the  superior  planets. 

Let  A,  B,  C,  Fig.  62,  page  294,  represent  the  earth 
in  different  positions  in  its  orbit,  M,  a  superior  planet,  as 
Mars,  and  N  R,  an  arc  of  the  concave  sphere  of  the  heav- 
ens. First,  suppose  the  planet  to  remain  at  rest  in  M, 
and  let  us  see  what  apparent  motions  it  will  receive  from 
the  real  motions  of  the  earth.  When  the  earth  is  at  B, 
it  will  see  the  planet  in  the  heavens  at  N  ;  and  as  the 
earth  moves  successively  through  C,  D,  E,  F,  the  planet 
will  appear  to  move  through  O,  P,  Q,  R.  B  and  F  are  the 
two  points  of  greatest  elongation  of  the  earth  from  the 
sun,  as  seen  from  the  planet ;  hence,  between  these 
25* 


294 


LETTERS   ON  ASTRONOMY. 


two  points,  while  passing  through  its  orbit  most  remote 
from  the  planet,  (when  the  planet  is  seen  in  superior 
conjunction,)  the  earth,  by  its  own  motion,  gives  an 
apparent  motion  to  the  planet  in  the  order  of  the  signs  ; 
that  is,  the  apparent  motion  given  by  the  real  motion 
of  the  earth  is  direct.  But  in  passing  from  F  to  B 
through  A,  when  the  planet  is  seen  in  opposition,  the 
apparent  motion  given  to  the  planet  by  the  earth's  mo- 
tion is  from  R  to  N,  and  is  therefore  retrograde.  As 
the  arc  described  by  the  earth,  when  the  motion  is  di- 
rect, is  much  greater  than  when  the  motion  is  retro- 
grade, while  the  apparent  arc  of  the  heavens  described 
by  the  planet  from  N  to  R,  in  the  one  case,  and  from 
R  to  N,  in  the  other,  is  the  same  in  both  cases,  the  ret- 
rograde motion  is  much  swifter  than  the  direct,  being 
performed  in  much  less  time. 

But  the  superior  planets  are  not  in  fact  at  rest,  as  we 
have  supposed,  but  are  all  the  while  moving  eastward, 
though  with  a  slower  motion  than  the  earth.  Indeed, 


PLANETARY  MOTIONS.  295 

with  respect  to  the  remotest  planets,  as  Saturn  and 
Uranus,  the  forward  motion  is  so  exceedingly  slow,  that 
the  above  representation  is  nearly  true  for  a  single  year. 
Still ,  the  effect  of  the  real  motions  of  all  the  superior  plan- 
ets, eastward,  is  to  increase  the  direct  apparent  motion 
communicated  by  the  earth,  and  to  diminish  the  retro- 
grade motion.  This  will  be  evident  from  inspecting 
the  figure ;  for  if  the  planet  actually  moves  eastward 
while  it  is  apparently  carried  eastward  by  the  earth's 
motion,  the  whole  motion  eastward  will  be  equal  to  the 
sum  of  the  two ;  and  if,  while  it  is  really  moving  east- 
ward, it  is  apparently  carried  westward  still  more  by  the 
earth's  motion,  the  retrograde  movement  will  equal  the 
difference  of  the  two. 

If  Mars  stood  still  while  the  earth  went  round  the 
sun,  then  a  second  opposition,  as  at  A,  would  occur  at 
the  end  of  one  year  from  the  first ;  but,  while  the  earth 
is  performing  this  circuit,  Mars  is  also  moving  the 
same  way,  more  than  half  as  fast ;  so  that,  when  the 
earth  returns  to  A,  the  planet  has  already  performed 
more  than  half  the  same  circuit,  and  will  have  complet- 
ed its  whole  revolution  before  the  earth  comes  up  with 
it.  Indeed  Mars,  after  having  been  seen  once  in  oppo- 
sition, does  not  come  into  opposition  again  until  after 
two  years  and  fifty  days.  And  since  the  planet  is  then 
comparatively  near  to  us,  as  at  M,  while  the  earth  is  at 
A,  and  appears  very  large  and  bright,  rising  unexpect- 
edly about  the  time  the  sun  sets,  he  surprises  the  world 
as  though  it  were  some  new  celestial  body.  But  on 
account  of  the  slow  progress  of  Saturn  and  Uranus,  we 
find,  after  having  performed  one  circuit  around  the  sun, 
that  they  are  but  little  advanced  beyond  where  we  left 
them  at  the  last  opposition.  The  time  between  one 
opposition  of  Saturn  and  another  is  only  a  year  and 
thirteen  days. 

It  appears,  therefore,  that  the  superior  planets  stead- 
ily pursue  their  course  around  the  sun,  but  that  their 
apparent  retrograde  motion,  when  in  opposition,  is  occa- 
sioned by  our  passing  by  them  with  a  swifter  motion,  of 


296  LETTERS  ON  ASTRONOMY. 

which  we  are  unconscious,  like  the  apparent  backward 
motion  of  a  vessel,  when  we  overtake  it  and  pass  by  it 
rapidly  in  a  steam-boat. 

Such  are  the  real  and  the  apparent  motions  of  the 
planets.  Let  us  now  turn  our  attention  to  the  laws  of 
the  planetary  orbits. 

There  are  three  great  principles,  according  to  which 
the  motions  of  the  earth  and  all  the  planets  around  the 
sun  are  regulated,  called  KEPLER'S  LAWS,  having  been 
first  discovered  by  the  astronomer  whose  name  they 
bear.  They  may  appear  to  you,  at  first,  dry  and  ob- 
scure ;  yet  they  will  be  easily  understood  from  the  ex- 
planations which  follow ;  and  so  important  have  they 
proved  in  astronomical  inquiries,  that  they  have  ac- 
quired for  their  renowned  discoverer  the  appellation  of 
the  'Legislator  of  the  Skies.1  We  will  consider  each 
of  these  laws  separately  ;  and,  for  the  sake  of  rendering 
the  explanation  clear  and  intelligible,  I  shall  perhaps 
repeat  some  things  that  have  been  briefly  mentioned 
before. 

FIRST  LAW. — The  orbits  of  the  earth  and  all  the 
planets  are  ellipses,  having  the  sun  in  the  common 
focus.  In  a  circle,  all  the  diameters  are  equal  to  one 
another ;  but  if  we  take  a  metallic  wire  or  hoop,  and 
draw  it  out  on  opposite  sides,  we  elongate  it  into  an 
ellipse,  of  which  the  different  diameters  are  very  une- 
qual. That  which  connects  the  points  most  distant 
from  each  other  is  called  the  transverse,  and  that  which 
is  at  right  angles  to  this  is  called  the  conjugate,  axis. 
Thus,  A  B,  Fig.  63,  is  the  transverse  axis,  and  C  D, 
the  conjugate  of  the  ellipse  ABC.  By  such  a  proc- 
ess of  elongating  the  circle  into  an  ellipse,  the  centre 
of  the  circle  may  be  conceived  of  as  drawn  opposite 
ways  to  E  and  F,  each  of  which  becomes  a  focus,  and 
both  together  are  called  the  foci  of  the  ellipse.  The 
distance  G  E,  or  G  F,  of  the  focus  from  the  centre  is 
called  the  eccentricity  of  the  ellipse ;  and  the  ellipse  is 
said  to  be  more  or  less  eccentric,  as  the  distance  of  the 
focus  from  the  centre  is  greater  or  less.  Figure  64, 


297 


represents  such  a  collection  of  ellipses  around  the  com- 
mon focus  F,  the  innermost,  A  G  D,  having  a  small  ec- 
centricity, or  varying  little  from  a  circle,  while  the  out- 
ermost, A  C  B,  is  an  eccentric  ellipse.  The  orbits  of  all 
the  bodies  that  revolve  about  the  sun,  both  planets 
and  comets,  have,  in  like  manner,  a  common  focus,  in 
which  the  sun  is  situated,  but  they  differ  in  eccentricity. 
Most  of  the  planets  have  orbits  of  very  little  eccentric- 


298 


LETTERS   ON  ASTRONOMY. 


ity,  differing  little  from  circles,  but  comets  move  in  very 
eccentric  ellipses.  The  earth's  path  around  the  sun 
varies  so  little  from  a  circle,  that  a  diagram  represent- 
ing it  truly  would  scarcely  be  distinguished  from  a  per- 
fect circle  ;  yet,  when  the  comparative  distances  of  the 
sun  from  the  earth  are  taken  at  different  seasons  of  the 
year,  we  find  that  the  difference  between  their  greatest 
and  least  distances  is  no  less  than  three  millions  of  miles. 

SECOND  LAW. — The  radius  vector  of  the  earth,  or 
of  any  planet,  describes  equal  areas  in  equal  times. 
You  will  recollect  that  the  radius  vector  is  a  line  drawn 
from  the  centre  of  the  sun  to  a  planet  revolving  about 
the  sun.  This  definition  I  have  somewhere  given  you 
before,  and  perhaps  it  may  appear  to  you  like  needless 
repetition  to  state  it  again.  In  a  book  designed  for 
systematic  instruction,  where  all  the  articles  are  dis- 
tinctly numbered,  it  is  commonly  sufficient  to  make  a 
reference  back  to  the  article  where  the  point  in  ques- 
tion is  explained  ;  but  I  think,  in  Letters  like  these,  you 
will  bear  with  a  little  repetition,  rather  than  be  at  the 
trouble  of  turning  to  the  Index  and  hunting  up  a  defi- 
nition long  since  given. 

In  Figure  65,  E  a,  E  6,  E  c,  &c.,  are  successive  repre- 
sentations of  the  radius  vector.  Now,  if  a  planet  sets 

Fig.  65. 


i/ 


iff 


299 

out  from  #,  and  travels  round  the  sun  in  the  direction 
of  a  b  c,  it  will  move  faster  when  nearer  the  sun,  as  at  a, 
than  when  more  remote  from  it,  as  at  m ;  yet,  if  a  & 
and  m  n  be  arcs  described  in  equal  times,  then,  accord- 
ing to  the  foregoing  law,  the  space  E  a  b  will  be  equal 
to  the  space  Emn\  and  the  same  is  true  of  all  the 
other  spaces  described  in  equal  times.  Although  the 
figure  E  a  b  is  much  shorter  than  E  m  n,  yet  its  greater 
breadth  exactly  counterbalances  the  greater  length  of 
those  figures  which  are  described  by  the  radius  vector 
where  it  is  longer. 

THIRD  LAW. — The  squares  of  the  periodical  times 
are  as  the  cubes  of  the  mean  distances  from  the  sun. 
The  periodical  time  of  a  body  is  the  time  it  takes  to 
complete  its  orbit,  in  its  revolution  about  the  sun. 
Thus  the  earth's  periodic  time  is  one  year,  and  that 
of  the  planet  Jupiter  about  twelve  years.  As  Jupiter 
takes  so  much  longer  time  to  travel  round  the  sun  than 
the  earth  does,  we  might  suspect  that  his  orbit  is  larger 
than  that  of  the  earth,  and  of  course,  that  he  is  at  a 
greater  distance  from  the  sun  ;  and  our  first  thought 
might  be,  that  he  is  probably  twelve  times  as  far  off; 
but  Kepler  discovered  that  the  distance  does  not  in- 
crease as  fast  as  the  times  increase,  but  that  the  planets 
which  are  more  distant  from  the  sun  actually  move 
slower  than  those  which  are  nearer.  After  trying  a 
great  many  proportions,  he  at  length  found  that,  if  we 
take  the  squares  of  the  periodic  times  of  two  planets, 
the  greater  square  contains  the  less,  just  as  often  as 
the  cube  of  the  distance  of  the  greater  contains  that 
of  the  less.  This  fact  is  expressed  by  saying,  that  the 
squares  of  the  periodic  times  are  to  one  another  as  the 
cubes  of  the  distances. 

This  law  is  of  great  use  in  determining  the  distance 
of  the  planets  from  the  sun.  Suppose,  for  example, 
that  we  wish  to  find  the  distance  of  Jupiter.  We  can 
easily  determine,  from  observation,  what  is  Jupiter's  pe- 
riodical time,  for  we  can  actually  see  how  long  it  takes 
for  Jupiter,  after  leaving  a  certain  part  of  the  heavens, 


300  LETTERS  ON  ASTRONOMY. 

to  come  round  to  the  same  part  again.  Let  this  pe- 
riod be  twelve  years.  The  earth's  period  is  of  course 
one  year ;  and  the  distance  of  the  earth,  as  determined 
from  the  sun's  horizontal  parallax,  as  already  explained, 
is  about  ninety-five  millions  of  miles.  Now,  we  have 
here  three  terms  of  a  proportion  to  find  the  fourth,  and 
therefore  the  solution  is  merely  a  simple  case  of  the 
rule  of  three.  Thus : — the  square  of  1  year :  square 
of  12  years  :  :  cube  of  95,000,000  :  cube  of  Jupiter's 
distance.  The  three  first  terms  being  known,  we  have 
only  to  multiply  together  the  second  and  third  and  di- 
vide by  the  first,  to  obtain  the  fourth  term,  which  will 
give  us  the  cube  of  Jupiter's  distance  from  the  sun  ;  and 
by  extracting  the  cube  root  of  this  sum,  we  obtain  the 
distance  itself.  In  the  same  manner  we  may  obtain  the 
respective  distances  of  all  the  other  planets. 

So  truly  is  this  a  law  of  the  solar  system,  that  it 
holds  good  in  respect  to  the  new  planets,  which  have 
been  discovered  since  Kepler's  time,  as  well  as  in  the 
case  of  the  old  planets.  It  also  holds  good  in  respect 
to  comets,  and  to  all  bodies  belonging  to  the  solar  sys- 
tem, which  revolve  around  the  sun  as  their  centre  of 
motion.  Hence,  it  is  justly  regarded  as  one  of  the 
most  interesting  and  important  principles  yet  develop- 
ed in  astronomy. 

But  who  was  this  Kepler,  that  gained  such  an  extra- 
ordinary insight  into  the  laws  of  the  planetary  system, 
as  to  be  called  the  '  Legislator  of  the  Skies  ?'  John 
Kepler  was  one  of  the  most  remarkable  of  the  human 
race,  and  I  think  I  cannot  gratify  or  instruct  you  more, 
than  by  occupying  the  remainder  of  this  Letter  with 
some  particulars  of  his  history. 

Kepler  was  a  native  of  Germany.  He  was  born  in 
the  Duchy  of  Wurtemberg,  in  1571.  As  Copernicus, 
Tycho  Brahe,  Galileo,  Kepler,  and  Newton,  are  names 
that  are  much  associated  in  the  history  of  astronomy, 
let  us  see  how  they  stood  related  to  each  other  in  point 
of  time.  Copernicus  was  bom  in  1473  ;  Tycho,  in 
1546  ;  Galileo,  in  1564  ;  Kepler,  in  1571 ;  and  Newton, 


KEPLER.  301 

in  1642.  Hence,  Copernicus  was  seventy-three  years 
before  Tycho,  and  Tycho  ninety-six  years  before  New- 
ton. They  all  lived  to  an  advanced  age,  so  that  Ty- 
cho, Galileo,  and  Kepler,  were  contemporary  for  many 
years;  and  Newton,  as  I  mentioned  in  the  sketch  I 
gave  you  of  his  life,  was  born  the  year  that  Galileo  died. 

Kepler  was  born  of  parents  who  were  then  in  hum- 
ble circumstances,  although  of  noble  descent.  Their 
misfortunes,  which  had  reduced  them  to  poverty,  seem 
to  have  been  aggravated  by  their  own  unhappy  disposi- 
tions ;  for  his  biographer  informs  us,  that  "  his  mother 
was  treated  with  a  degree  of  barbarity  by  her  husband 
and  brother-in-law,  that  was  hardly  exceeded  by  her 
own  perverseness."  It  is  fortunate,  therefore,  that  Kep- 
ler, in  his  childhood,  was  removed  from  the  immediate 
society  and  example  of  his  parents,  and  educated  at  a 
public  school  at  the  expense  of  the  Duke  of  Wurtem- 
berg.  He  early  imbibed  a  taste  for  natural  philosophy, 
but  had  conceived  a  strong  prejudice  against  astrono- 
my, and  even  a  contempt  for  it,  inspired,  probably,  by 
the  arrogant  and  ridiculous  pretensions  of  the  astrolo- 
gers, who  constituted  the  principal  astronomers  of  his 
country.  A  vacant  post,  however,  of  teacher  of  as- 
tronomy, occurred  when  he  was  of  a  suitable  age  to  fill 
it,  and  he  was  compelled  to  take  it  by  the  authority  of 
his  tutors,  though  with  many  protestations,  on  his  part, 
wishing  to  be  provided  for  in  some  other  more  brilliant 
profession. 

Happy  is  genius,  when  it  lights  on  a  profession  en- 
tirely consonant  to  its  powers,  where  the  objects  suc- 
cessively presented  to  it  are  so  exactly  suited  to  its  na- 
ture, that  it  clings  to  them  as  the  loadstone  to  its  kin- 
dred metal  among  piles  of  foreign  ores.  Nothing  could 
have  been  more  congenial  to  the  very  mental  constitu- 
tion of  Kepler,  than  the  study  of  astronomy, — a  science 
where  the  most  capacious  understanding  may  find  scope 
in  unison  with  the  most  fervid  imagination. 

Much  as  has  been  said  against  hypotheses  in  philos- 
ophy, it  is  nevertheless  a  fact,  that  some  of  the  greatest 
26  L.  A. 


302  LETTERS  ON  ASTRONOMY. 

truths  have  been  discovered  in  the  pursuit  of  hypoth- 
eses, in  themselves  entirely  false  ;  truths,  moreover,  far 
more  important  than  those  assumed  by  the  hypotheses ; 
as  Columbus,  in  searching  for  a  northwest  passage  to 
India,  discovered  a  new  world.  Thus  Kepler  groped 
his  way  through  many  false  and  absurd  suppositions,  to 
some  of  the  most  sublime  discoveries  ever  made  by 
man.  The  fundamental  principle  which  guided  him 
was  not,  however,  either  false  or  absurd.  It  was,  that 
God,  who  made  the  world,  had  established,  throughout 
all  his  works,  fixed  laws, — laws  that  are  often  so  defi- 
nite as  to  be  capable  of  expression  in  exact  numerical 
terms.  In  accordance  with  these  views,  he  sought  for 
numerical  relations  in  the  disposition  and  arrangement 
of  the  planets,  in  respect  to  their  number,  the  times  of 
their  revolution,  and  their  distances  from  one  another. 
Many,  indeed,  of  the  subordinate  suppositions  which 
he  made,  were  extremely  fanciful  ;  but  he  tried  his  own 
hypotheses  by  a  rigorous  mathematical  test,  wherever 
he  could  apply  it ;  and  as  soon  as  he  discovered  that  a 
supposition  would  not  abide  this  test,  he  abandoned  it 
without  the  least  hesitation,  and  adopted  others,  which 
he  submitted  to  the  same  severe  trial,  to  share,  perhaps, 
the  same  fate.  "  After  many  failures,"  he  says,  "  I  was 
comforted  by  observing  that  the  motions,  in  every  case, 
seemed  to  be  connected  with  the  distances  ;  and  that, 
when  there  was  a  great  gap  between  the  orbits,  there 
was  the  same  between  the  motions.  And  I  reasoned 
that,  if  God  had  adapted  motions  to  the  orbits  in  some 
relation  to  the  distances,  he  had  also  arranged  the  dis- 
tances themselves  in  relation  to  something  else." 

In  two  years  after  he  commenced  the  study  of  as- 
tronomy, he  published  a  book,  called  the  '  Mysterium 
Cosmographicwm,'  a  name  which  implies  an  explana- 
tion of  the  mysteries  involved  in  the  construction  of  the 
universe.  This  work  was  full  of  the  wildest  specula- 
tions and  most  extravagant  hypotheses,  the  most  re- 
markable of  which  was,  that  the  distances  of  the  plan- 
ets from  the  sun  are  regulated  by  the  relations  which 


KEPLER.  303 

subsist  between  the  five  regular  solids.  It  is  well 
known  to  geometers,  that  there  are  and  can  be  only 
five  regular  solids.  These  are,  first,  the  tetraedron,  a 
four-sided  pyramid,  all  whose  sides  are  equal  and  simi- 
lar triangles ;  secondly,  the  cube,  contained  by  six 
equal  squares ;  thirdly,  an  octaedron,  an  eight-sided 
figure,  consisting  of  two  tetraedrons  joined  together  at 
their  bases  ;  fourthly,  a  dedecaedron,  having  twelve  five- 
sided  or  pentagonal  faces ;  and,  fifthly,  an  icosaedron, 
contained  by  twenty  equal  and  similar  triangles.  You 
will  be  much  at  a  loss,  I  think,  to  imagine  what  rela- 
tion Kepler  could  trace  between  these  strange  figures 
and  the  distances  of  the  several  planets  from  the  sun. 
He  thought  he  discovered  a  connexion  between  those 
distances  and  the  spaces  which  figures  of  this  kind 
would  occupy,  if  interposed  in  certain  ways  between 
them.  Thus,  he  says  the  Earth  is  a  circle,  the  meas- 
ure of  all ;  round  it  describe  a  dodecaedron,  and  the 
circle  including  this  will  be  the  orbit  of  Mars.  Round 
this  circle  describe  a  tetraedron,  and  the  circle  inclu- 
ding this  will  be  the  orbit  of  Jupiter.  Describe  a  cube 
round  this,  and  the  circle  including  it  will  be  the  orbit 
of  Saturn.  Now,  inscribe  in  the  earth  an  icosaedron, 
and  the  circle  included  in  this  will  give  the  orbit  of 
Venus.  In  this  inscribe  an  octaedron,  and  the  circle 
included  in  this  will  be  the  orbit  of  Mercury.  On  this 
supposed  discovery  Kepler  exults  in  the  most  enthusi- 
astic expressions.  "The  intense  pleasure  I  have  re- 
ceived from  this  discovery  never  can  be  told  in  words. 
I  regretted  no  more  time  wasted ;  I  tired  of  no  labor ; 
I  shunned  no  toil  of  reckoning ;  days  and  nights  I  spent 
in  calculations,  until  I  could  see  whether  this  opinion 
would  agree  with  the  orbits  of  Copernicus,  or  whether 
my  joy  was  to  vanish  into  air.  I  willingly  subjoin  that 
sentiment  of  Archytas,  as  given  by  Cicero  ;  '  If  I  could 
mount  up  into  heaven,  and  thoroughly  perceive  the 
nature  of  the  world  and  the  beauty  of  the  stars,  that 
admiration  would  be  without  a  charm  for  me,  unless  I 
had  some  one  like  you,  reader,  candid,  attentive,  and 


304  LETTERS  ON  ASTRONOMY. 

eager  for  knowledge,  to  whom  to  describe  it.'  If  you 
acknowledge  this  feeling,  and  are  candid,  you  will  re- 
frain from  blame,  such  as,  not  without  cause,  I  antici- 
pate ;  but  if,  leaving  that  to  itself,  you  fear,  lest  these 
things  be  not  ascertained,  and  that  I  have  shouted  tri- 
umph before  victory,  at  least  approach  these  pages, 
and  learn  the  matter  in  consideration :  you  will  not 
find,  as  just  now,  new  and  unknown  planets  interpos- 
ed ;  that  boldness  of  mine  is  not  approved ;  but  those 
old  ones  very  little  loosened,  and  so  furnished  by  the 
interposition  (however  absurd  you  may  think  it)  of  rec- 
tilinear figures,  that  in  future  you  may  give  a  reason 
to  the  rustics,  when  they  ask  for  the  hooks  which  keep 
the  skies  from  falling." 

When  Tycho  Brahe,  who  had  then  retired  from  his 
famous  Uraniburg,  and  was  settled  in  Prague,  met  with 
this  work  of  Kepler's,  he  immediately  recognised  under 
this  fantastic  garb  the  lineaments  of  a  great  astronomer. 
He  needed  such  an  unwearied  and  patient  calculator 
as  he  perceived  Kepler  to  be,  to  aid  him  in  his  labors, 
in  order  that  he  might  devote  himself  more  unreserved- 
ly to  the  taking  of  observations, — an  employment  in 
which  he  delighted,  and  in  which,  as  I  mentioned,  in 
giving  you  a  sketch  of  his  history,  he  excelled  all 
men  of  that  and  preceding  ages.  Kepler,  therefore,  at 
the  express  invitation  of  Tycho,  went  to  Prague,  and 
joined  him  in  the  capacity  of  assistant.  Had  Tycho 
been  of  a  nature  less  truly  noble,  he  might  have  looked 
with  contempt  on  one  who  had  made  so  few  observa- 
tions, and  indulged  so  much  in  wild  speculation  ;  or  he 
might  have  been  jealous  of  a  rising  genius,  in  which  he 
descried  so  many  signs  of  future  eminence  as  an  as- 
tronomer ;  but,  superior  to  all  the  baser  motives,  he 
extends  to  the  young  aspirant  the  hand  of  encourage- 
ment, in  the  following  kind  invitation :  "  Come  not  as 
a  stranger,  but  as  a  very  welcome  friend  ;  come,  and 
share  in  my  observations,  with  such  instruments  as  I 
have  with  me." 

Several  years  previous  to  this,  Kepler,  after  one  or 


KEPLER.  305 

two  unsuccessful  trials,  had  found  him  a  wife,  from 
whom  he  expected  a  considerable  fortune ;  but  in  this 
he  was  disappointed ;  and  so  poor  was  he,  that,  when 
on  his  journey  to  Prague,  in  company  with  his  wife, 
being  taken  sick,  he  was  unable  to  defray  the  expenses 
of  the  journey,  and  was  forced  to  cast  himself  on  the 
bounty  of  Tycho. 

In  the  course  of  the  following  year,  while  absent  from 
Prague,  he  fancied  that  Tycho  had  injured  him,  and 
accordingly  addressed  to  the  noble  Dane  a  letter  full 
of  insults  and  reproaches.  A  mild  reply  from  Tycho 
opened  the  eyes  of  Kepler  to  his  own  ingratitude.  His 
better  feelings  soon  returned,  and  he  sent  to  his  great 
patron  this  humble  apology:  "Most  noble  Tycho! 
How  shall  I  enumerate,  or  rightly  estimate,  your  bene- 
fits conferred  on  me !  For  two  months  you  have  lib- 
erally and  gratuitously  maintained  me,  and  my  whole 
family  ;  you  have  provided  for  all  my  wishes  ;  you  have 
done  me  every  possible  kindness  ;  you  have  communi- 
cated to  me  every  thing  you  hold  most  dear  ;  no  one,  by 
word  or  deed,  has  intentionally  injured  me  in  any  thing ; 
in  short,  not  to  your  own  children,  your  wife,  or  your- 
self, have  you  shown  more  indulgence  than  to  me. 
This  being  so,  as  I  am  anxious  to  put  upon  record,  I 
cannot  reflect,  without  consternation,  that  I  should  have 
been  so  given  up  by  God  to  my  own  intemperance,  as 
to  shut  my  eyes  on  all  these  benefits ;  that,  instead  of 
modest  and  respectful  gratitude,  I  should  indulge  for 
three  weeks  in  continual  moroseness  towards  all  your 
family,  and  in  headlong  passion  and  the  utmost  inso- 
lence towards  yourself,  who  possess  so  many  claims  on 
my  veneration,  from  your  noble  family,  your  extraordi- 
nary learning,  and  distinguished  reputation.  Whatever 
I  have  said  or  written  against  the  person,  the  fame,  the 
honor,  and  the  learning,  of  your  Excellency ;  or  what- 
ever, in  any  other  way,  I  have  injuriously  spoken  or 
written,  (if  they  admit  no  other  more  favorable  inter- 
pretation,) as  to  my  grief  I  have  spoken  and  written 
many  things,  and  more  than  I  can  remember ;  all  and 
26* 


306  LETTERS   ON  ASTRONOMY. 

every  thing  I  recant,  and  freely  and  honestly  declare  and 
profess  to  be  groundless,  false,  and  incapable  of  proof." 
This  was  ample  satisfaction  to  the  generous  Tycho. 

"  To  err  is  human  :  to  forgive,  divine." 

On  Kepler's  return  to  Prague,  he  was  presented  to 
the  Emperor  by  Tycho,  and  honored  with  the  title  of 
Imperial  Mathematician.  This  was  in  1601,  when  he 
was  thirty  years  of  age.  Tycho  died  shortly  after,  and 
Kepler  succeeded  him  as  principal  mathematician  to 
the  Emperor ;  but  his  salary  was  badly  paid,  and  he 
suffered  much  from  pecuniary  embarrassments.  Al- 
though he  held  the  astrologers,  or  those  who  told  for- 
tunes by  the  stars,  in  great  contempt,  yet  he  entertained 
notions  of  his  own,  on  the  same  subject,  quite  as  ex- 
travagant, and  practised  the  art  of  casting  nativities,  to 
eke  out  a  support  for  his  family. 

When  Galileo  began  to  observe  with  his  telescope, 
and  announced,  in  rapid  succession,  his  wonderful  dis- 
coveries, Kepler  entered  into  them  with  his  character- 
istic enthusiasm,  although  they  subverted  many  of  his 
favorite  hypotheses.  But  such  was  his  love  of  truth, 
that  he  was  among  the  first  to  congratulate  Galileo,  and 
a  most  engaging  correspondence  was  carried  on  between 
these  master-spirits. 

The  first  planet,  which  occupied  the  particular  atten- 
tion of  Kepler,  was  Mars,  the  long  and  assiduous  study 
of  whose  motions  conducted  him  at  length  to  the  dis- 
covery of  those  great  principles  called  c  Kepler's  Laws.7 
Rarely  do  we  meet  with  so  remarkable  a  union  of  a 
vivid  fancy  with  a  profound  intellect.  The  hasty  and 
extravagant  suggestions  of  the  former  were  submitted 
to  the  most  laborious  calculations,  some  of  which,  that 
were  of  great  length,  he  repeated  seventy  times.  This 
exuberance  of  fancy  frequently  appears  in  his  style  of 
writing,  which  occasionally  assumes  a  tone  ludicrously 
figurative.  He  seems  constantly  to  contemplate  Mars 
as  a  valiant  hero,  who  had  hitherto  proved  invincible, 
and  who  would  often  elude  his  own  efforts  to  conquer 


KEPLER.  307 

him.  "  While  thus  triumphing  over  Mars,  and  prepar- 
ing for  him,  as  for  one  altogether  vanquished,  tabular 
prisons,  and  equated,  eccentric  fetters,  it  is  buzzed 
here  and  there,  that  the  victory  is  vain,  and  that  the 
war  is  raging  anew  as  violently  as  before.  For  the  ene- 
my, left  at  home  a  despised  captive,  has  burst  all  the 
chains  of  the  equation,  and  broken  forth  of  the  prisons 
of  the  tables.  Skirmishes  routed  my  forces  of  physical 
causes,  and,  shaking  off  the  yoke,  regained  their  liberty. 
And  now,  there  was  little  to  prevent  the  fugitive  enemy 
from  effecting  a  junction  with  his  own  rebellious  sup- 
porters, and  reducing  me  to  despair,  had  I  not  sudden- 
ly sent  into  the  field  a  reserve  of  new  physical  reason- 
ings, on  the  rout  and  dispersion  of  the  veterans,  and 
diligently  followed,  without  allowing  the  slightest  res- 
pite, in  the  direction  in  which  he  had  broken  out." 

But  he  pursued  this  warfare  with  the  planet  until  he 
gained  a  full  conquest,  by  the  discovery  of  the  first  two 
of  his  laws,  namely,  that  he  revolves  in  an  elliptical 
orbit,  and  that  his  radius  vector  passes  over  equal 
spaces  in  equal  times. 

Domestic  troubles,  however,  involved  him  in  the 
deepest  affliction.  Poverty,  the  loss  of  a  promising  and 
favorite  son,  the  death  of  his  wife,  after  a  long  illness ; 
— these  were  some  of  the  misfortunes  that  clustered 
around  him.  Although  his  first  marriage  had  been  an 
unhappy  one,  it  was  not  consonant  to  his  genius  to 
surrender  any  thing  with  only  a  single  trial.  Accord- 
ingly, it  was  not  long  before  he  endeavored  to  repair 
his  loss  by  a  second  alliance.  He  commissioned  a 
number  of  his  friends  to  look  out  for  him,  and  he  soon 
obtained  a  tabular  list  of  eleven  ladies,  among  whom 
his  affections  wavered.  The  progress  of  his  courtship 
is  thus  narrated  in  the  interesting  'Life'  contained  in 
the  '  Library  of  Useful  Knowledge.'  It  furnishes  so 
fine  a  specimen  of  his  eccentricities,  that  I  cannot  deny 
myself  the  pleasure  of  transcribing  the  passage  for  your 
perusal.  It  is  taken  from  an  account  which  Kepler 
himself  gave  in  a  letter  to  a  friend. 


308  LETTERS  ON  ASTRONOMY. 

"  The  first  on  the  list  was  a  widow,  an  intimate  friend 
of  his  first  wife  and  who,  on  many  accounts,  appeared 
a  most  eligible  match.  At  first,  she  seemed  favorably 
inclined  to  the  proposal :  it  is  certain  that  she  took 
time  to  consider  it,  but  at  last  she  very  quietly  excused 
herself.  Finding  her  afterwards  less  agreeable  in  per- 
son than  he  had  anticipated,  he  considered  it  a  fortu- 
nate escape,  mentioning,  among  other  objections,  that 
she  had  two  marriageable  daughters,  whom,  by  the  way, 
he  had  got  on  his  list  for  examination.  He  was  much 
troubled  to  reconcile  his  astrology  with  the  fact  of  his 
having  taken  so  much  pains  about  a  negotiation  not 
destined  to  succeed.  He  examined  the  case  profes- 
sionally. '  Have  the  stars,'  says  he,  •'  exercised  any  in- 
fluence here  ?  For,  just  about  this  time,  the  direction 
of  the  mid-heaven  is  in  hot  opposition  to  Mars,  and  the 
passage  of  Saturn  through  the  ascending  point  of  the 
zodiac,  in  the  scheme  of  my  nativity,  will  happen  again 
next  November  and  December.  But,  if  these  are  the 
causes,  how  do  they  act  ?  Is  that  explanation  the  true 
one,  which  I  have  elsewhere  given  ?  For  I  can  never 
think  of  handing  over  to  the  stars  the  office  of  deities, 
to  produce  effects.  Let  us,  therefore,  suppose  it  ac- 
counted for  by  the  stars,  that  at  this  season  I  am  vio- 
lent in  my  temper  and  affections,  in  rashness  of  belief, 
in  a  show  of  pitiful  tender-heartedness,  in  catching  at 
reputation  by  new  and  paradoxical  notions,  and  the 
singularity  of  my  actions  ;  in  busily  inquiring  into,  and 
weighing,  and  discussing,  various  reasons ;  in  the  unea- 
siness of  my  mind,  with  respect  to  my  choice.  I  thank 
God,  that  that  did  not  happen  which  might  have  hap- 
pened ;  that  this  marriage  did  not  take  place.  Now 
for  the  others.'  Of  these,  one  was  too  old  ;  another,  in 
bad  health ;  another,  too  proud  of  her  birth  and  quar- 
terings ;  a  fourth  had  learned  nothing  but  showy  ac- 
complishments, not  at  all  suitable  to  the  kind  of  life  she 
would  have  to  lead  with  him.  Another  grew  impatient, 
and  married  a  more  decided  admirer  while  he  was  hes- 
itating. <  The  mischief,'  says  he,  '  in  all  these  attach- 


KEPLER.  309 

ments  was,  that,  whilst  I  was  delaying,  comparing,  and 
balancing,  conflicting  reasons,  every  day  saw  me  in- 
flamed with  a  new  passion.'  By  the  time  he  reached 
No.  8,  of  his  list,  he  found  his  match  in  this  respect. 
'  Fortune  has  avenged  herself  at  length  on  my  doubtful 
inclinations.  At  first,  she  was  quite  complying,  and 
her  friends  also.  Presently,  whether  she  did  or  did 
not  consent,  not  only  I,  but  she  herself,  did  not  know. 
After  the  lapse  of  a  few  days,  came  a  renewed  promise, 
which,  however,  had  to  be  confirmed  a  third  time  :  and, 
four  days  after  that,  she  again  repented  her  conforma- 
tion, and  begged  to  be  excused  from  it.  Upon  this,  I 
gave  her  up,  and  this  time  all  my  counsellors  were  of 
one  opinion.'  This  was  the  longest  courtship  in  the 
list,  having  lasted  three  whole  months ;  and,  quite  dis- 
heartened by  its  bad  success,  Kepler's  next  attempt  was 
of  a  more  timid  complexion.  His  advances  to  No.  9 
were  made  by  confiding  to  her  the  whole  story  of  his 
recent  disappointment,  prudently  determining  to  be 
guided  in  his  behavior,  by  observing  whether  the  treat- 
ment he  experienced  met  with  a  proper  degree  of  sym- 
pathy. Apparently,  the  experiment  did  not  succeed ; 
and,  when  almost  reduced  to  despair,  Kepler  betook 
himself  to  the  advice  of  a  friend,  who  had  for  some 
time  past  complained  that  she  was  not  consulted  in  this 
difficult  negotiation.  When  she  produced  No.  10,  and 
the  first  visit  was  paid,  the  report  upon  her  was  as  fol- 
lows :  '  She  has,  undoubtedly,  a  good  fortune,  is  of 
good  family,  and  of  economical  habits :  but  her  physi- 
ognomy is  most  horribly  ugly ;  she  would  be  stared  at 
in  the  streets,  not  to  mention  the  striking  disproportion 
in  our  figures.  I  am  lank,  lean,  and  spare ;  she  is 
short  and  thick.  In  a  family  notorious  for  fatness,  she 
is  considered  superfluously  fat.'  The  only  objection  to 
No.  1 1  seems  to  have  been,  her  excessive  youth ;  and 
when  this  treaty  was  broken  off,  on  that  account,  Kep- 
ler turned  his  back  upon  all  his  advisers,  and  chose  for 
himself  one  who  had  figured  as  No.  5,  in  his  list,  to 
whom  he  professes  to  have  felt  attached  throughout, 


310  LETTERS  ON  ASTRONOMY. 

but  from  whom  the  representations  of  his  friends  had 
hitherto  detained  him,  probably  on  account  of  her  hum- 
ble station." 

Having  thus  settled  his  domestic  affairs,  Kepler  now 
betook  himself,  with  his  usual  industry,  to  his  astro- 
nomical studies,  and  brought  before  the  world  the  most 
celebrated  of  his  publications,  entitled  'Harmonics.' 
In  the  fifth  book  of  this  work  he  announced  his  Third 
Law,- — that  the  squares  of  the  periodical  times  of  the 
planets  are  as  the  cubes  of  the  distances.  Kepler's 
rapture  on  detecting  it  was  unbounded.  "  What,"  says 
he,  "  I  prophesied  two-and-twenty  years  ago,  as  soon  as 
I  discovered  the  five  solids  among  the  heavenly  orbits ; 
what  I  firmly  believed  long  before  I  had  seen  Ptolemy's 
Harmonics  ;  what  I  had  promised  my  friends  in  the 
title  of  this  book,  which  I  named  before  I  was  sure  of 
my  discovery ;  what,  sixteen  years  ago,  I  urged  as  a 
thing  to  be  sought;  that  for  which  I  joined  Tycho 
Brahe,  for  which  I  settled  in  Prague,  for  which  I  have 
devoted  the  best  part  of  my  life  to  astronomical  con- 
templations ; — at  length  I  have  brought  to  light,  and 
have  recognised  its  truth  beyond  my  most  sanguine  ex- 
pectations. It  is  now  eighteen  months  since  I  got  the 
first  glimpse  of  light,  three  months  since  the  dawn,  very 
few  days  since  the  unveiled  sun,  most  admirable  to 
gaze  on,  burst  out  upon  me.  Nothing  holds  me :  I 
will  indulge  in  my  sacred  fury  ;  I  will  triumph  over 
mankind  by  the  honest  confession,  that  I  have  stolen 
the  golden  vases  of  the  Egyptians  to  build  up  a  taber- 
nacle for  my  God,  far  from  the  confines  of  Egypt.  If 
you  forgive  me,  I  rejoice :  if  you  are  angry,  I  can  bear 
it ;  the  die  is  cast,  the  book  is  written,  to  be  read  either 
now  or  by  posterity, — I  care  not  which.  I  may  well 
wait  a  century  for  a  reader,  as  God  has  waited  six 
thousand  years  for  an  observer."  In  accordance  with 
the  notion  he  entertained  respecting  the  "  music  of  the 
spheres,"  he  made  Saturn  and  Jupiter  take  the  bass, 
Mars  the  tenor,  the  Earth  and  Venus  the  counter,  and 
Mercury  the  treble, 


KEPLER.  311 

"  The  misery  in  which  Kepler  lived,"  says  Sir  David 
Brewster,  in  his  '  Life  of  Newton/  "  forms  a  painful 
contrast  with  the  services  which  he  performed  for  sci- 
ence. The  pension  on  which  he  subsisted  was  always  in 
arrears ;  and  though  the  three  emperors,  whose  reigns  he 
adorned,  directed  their  ministers  to  be  more  punctual 
in  its  payment,  the  disobedience  of  their  commands 
was  a  source  of  continual  vexation  to  Kepler.  When 
he  retired  to  Silesia,  to  spend  the  remainder  of  his  days, 
his  pecuniary  difficulties  became  still  more  harassing. 
Necessity  at  length  compelled  him  to  apply  personally 
for  the  arrears  which  were  due  ;  and  he  accordingly  set 
out,  in  1630,  when  nearly  sixty  years  of  age,  for  Rat- 
isbon  ;  but,  in  consequence  of  the  great  fatigue  which 
so  long  a  journey  on  horseback  produced,  he  was  seized 
with  a  fever,  which  put  an  end  to  his  life." 

Professor  Whewell  (in  his  interesting  work  on  As- 
tronomy and  General  Physics  considered  with  reference 
to  Natural  Theology)  expresses  the  opinion  that  Kep- 
ler, notwithstanding  his  constitutional  oddities,  was  a 
man  of  strong  and  lively  piety.  His  '  Commentaries  on 
the  Motions  of  Mars'  he  opens  with  the  following  pas- 
sage :  "I  beseech  my  reader,  that,  not  unmindful  of 
the  Divine  goodness  bestowed  on  man,  he  do  with  me 
praise  and  celebrate  the  wisdom  and  greatness  of  the 
Creator,  which  I  open  to  him  from  a  more  inward  ex- 
plication of  the  form  of  the  world,  from  a  searching  of 
causes,  from  a  detection  of  the  errors  of  vision ;  and 
that  thus,  not  only  in  the  firmness  and  stability  of  the 
earth,  he  perceive  with  gratitude  the  preservation  of 
all  living  things  in  Nature  as  the  gift  of  God,  but  also 
that  in  its  motion,  so  recondite,  so  admirable,  he  ac- 
knowledge the  wisdom  of  the  Creator.  But  him  who 
is  too  dull  to  receive  this  science,  or  too  weak  to  believe 
the  Copernican  system  without  harm  to  his  piety, — 
him,  I  say,  I  advise  that,  leaving  the  school  of  astrono- 
my, and  condemning,  if  he  please,  any  doctrines  of  the 
philosophers,  he  follow  his  own  path,  and  desist  from 
this  wandering  through  the  universe ;  and,  lifting  up 


LETTERS  ON  ASTRONOMY. 

his  natural  eyes,  with  which  he  alone  can  see,  pour 
himself  out  in  his  own  heart,  in  praise  of  God  the  Cre- 
ator ;  being  certain  that  he  gives  no  less  worship  to  God 
than  the  astronomer,  to  whom  God  has  given  to  see 
more  clearly  with  his  inward  eye,  and  who,  for  what 
he  has  himself  discovered,  both  can  and  will  glorify 
God." 

In  a  Life  of  Kepler,  very  recently  published  in  his 
native  country,  founded  on  manuscripts  of  his  which 
have  lately  been  brought  to  light,  there  are  given  nu- 
merous other  examples  of  a  similar  devotional  spirit. 
Kepler  thus  concludes  his  Harmonics :  "  I  give  Thee 
thanks,  Lord  and  Creator,  that  Thou  has  given  me  joy 
through  Thy  creation ;  for  I  have  been  ravished  with 
the  work  of  Thy  hands.  I  have  revealed  unto  mankind 
the  glory  of  Thy  works,  as  far  as  my  limited  spirit  could 
conceive  their  infinitude.  Should  I  have  brought  for- 
ward any  thing  that  is  unworthy  of  Thee,  or  should  I 
have  sought  my  own  fame,  be  graciously  pleased  to  for- 
give me." 

As  Galileo  experienced  the  most  bitter  persecutions 
from  the  Church  of  Rome,  so  Kepler  met  with  much  vio- 
lent opposition  and  calumny  from  the  Protestant  clergy 
of  his  own  country,  particularly  for  adopting,  in  an  al- 
manac which,  as  astronomer  royal,  he  annually  publish- 
ed, the  reformed  calendar,  as  given  by  the  Pope  of 
Rome.  His  opinions  respecting  religious  liberty,  also, 
appear  to  have  been  greatly  in  advance  of  the  times  in 
which  he  lived.  In  answer  to  certain  calumnies  with 
which  he  was  assailed,  for  his  boldness  in  reasoning 
from  the  light  of  Nature,  he  uttered  these  memorable 
words  :  "  The  day  will  soon  break,  when  pious  sim- 
plicity will  be  ashamed  of  its  blind  superstition  ;  when 
men  will  recognise  truth  in  the  book  of  Nature  as  well 
as  in  the  Holy  Scriptures,  and  rejoice  in  the  two  reve- 
lations." 


COMETS.  313 


LETTER  XXV. 


COMETS. 


1  Fancy  now  no  more 


Wantons  on  fickle  pinions  through  the  skies, 

But,  fixed  in  aim,  and  conscious  of  her  power, 

Sublime  from  cause  to  cause  exults  to  rise, 

Creation's  blended  stores  arranging  as  she  flies."— Beattie. 

NOTHING  in  astronomy  is  more  truly  admirable,  than 
the  knowledge  which  astronomers  have  acquired  of  the 
motions  of  comets,  and  the  power  they  have  gained  of 
predicting  their  return.  Indeed,  every  thing  appertain- 
ing to  this  class  of  bodies  is  so  wonderful,  as  to  seem 
rather  a  tale  of  romance  than  a  simple  recital  of  facts. 
Comets  are  truly  the  knights-errant  of  astronomy.  Ap- 
pearing suddenly  in  the  nocturnal  sky,  and  often  drag- 
ging after  them  a  train  of  terrific  aspect,  they  were,  in 
the  earlier  ages  of  the  world,  and  indeed  until  a  recent 
period,  considered  as  peculiarly  ominous  of  the  wrath 
of  Heaven,  and  as  harbingers  of  wars  and  famines,  of 
the  dethronement  of  monarchs,  and  the  dissolution  of 
empires. 

Science  has,  it  is  true,  disarmed  them  of  their  terrorsy 
and  demonstrated  that  they  are  under  the  guidance 
of  the  same  Hand,  that  directs  in  their  courses  the  oth- 
er members  of  the  solar  system  ;  but  she  has,  at  the 
same  time,  arrayed  them  in  a  garb  of  majesty  peculiar- 
ly her  own. 

Although  the  ancients  paid  little  attention  to  the  or- 
dinary phenomena  of  Nature,  hardly  deeming  them 
worthy  of  a  reason,  yet,  when  a  comet  blazed  forth, 
fear  and  astonishment  conspired  to  make  it  an  object 
of  the  most  attentive  observation.  Hence  the  aspects 
of  remarkable  comets,  that  have  appeared  at  various 
times,  have  been  handed  down  to  us,  often  with  cir- 
cumstantial minuteness,  by  the  historians  of  different 
ages.  The  comet  which  appeared  in  the  year  130,  be- 
fore the  Christian  era,  at  the  birth  of  Mithridates,  is 
27  L.  A. 


314  LETTERS  ON  ASTRONOMY. 

said  to  have  had  a  disk  equal  in  magnitude  to  that  of 
the  sun.  Ten  years  before  this,  one  was  seen,  which, 
according  to  Justin,  occupied  a  fourth  part  of  the  sky, 
that  is,  extended  over  forty-five  degrees,  and  surpassed 
the  sun  in  splendor.  In  the  year  400,  one  was  seen 
which  resembled  a  sword  in  shape,  and  extended  from 
the  zenith  to  the  horizon. 

Such  are  some  of  the  accounts  of  comets  of  past 
ages ;  but  it  is  probable  we  must  allow  much  for  the 
exaggerations  naturally  accompanying  the  descriptions 
of  objects  in  themselves  so  truly  wonderful. 

A  comet,  when  perfectly  formed,  consists  of  three 
parts,  the  nucleus,  the  envelope,  and  the  tail.  The  nu- 
cleus, or  body  of  the  comet,  is  generally  distinguished  by 
its  forming  a  bright  point  in  the  centre  of  the  head,  con- 
veying the  idea  of  a  solid,  or  at  least  of  a  very  dense, 
portion  of  matter.  Though  it  is  usually  exceedingly 
small,  when  compared  with  the  other  parts  of  the  comet, 
and  is  sometimes  wanting  altogether,  yet  it  occasionally 
subtends  an  angle  capable  of  being  measured  by  the 
telescope.  The  envelope  (sometimes  called  the  coma, 
from  a  Latin  word  signifying  hair,  in  allusion  to  its  hairy 
appearance)  is  a  dense  nebulous  covering,  which  fre- 
quently renders  the  edge  of  the  nucleus  so  indistinct, 
that  it  is  extremely  difficult  to  ascertain  its  diameter 
with  any  degree  of  precision.  Many  comets  have  no 
nucleus,  but  present  only  a  nebulous  mass,  exceedingly 
attenuated  on  the  confines,  but  gradually  increasing  in 
density  towards  the  centre.  Indeed,  there  is  a  regular 
gradation  of  comets,  from  such  as  are  composed  mere- 
ly of  a  gaseous  or  vapory  medium,  to  those  which  have 
a  well-defined  nucleus.  In  some  instances  on  record, 
astronomers  have  detected  with  their  telescopes  small 
stars  through  the  densest  part  of  a  comet.  The  tail  is 
regarded  as  an  expansion  or  prolongation  of  the  coma  ; 
and  presenting,  as  it  sometimes  does,  a  train  of  appall- 
ing magnitude,  and  of  a  pale,  portentous  light,  it  con- 
fers on  this  class  of  bodies  their  peculiar  celebrity. 
These  several  parts  are  exhibited  in  Fig.  67,  which 


Figures  67,  68. 


COMETS  OF   168O  AND   1811 


COMETS.  315 

represents  the  appearance  of  the  comet  of  1680.  Fig. 
68  also  exhibits  that  of  the  comet  of  1811. 

The  number  of  comets  belonging  to  the  solar  system, 
is  probably  very  great.  Many  no  doubt  escape  obser- 
vation, by  being  above  the  horizon  in  the  day-time. 
Seneca  mentions,  that  during  a  total  eclipse  of  the  sun, 
which  happened  sixty  years  before  the  Christian  era,  a 
large  and  splendid  comet  suddenly  made  its  appear- 
ance, being  very  near  the  sun.  The  leading  particu- 
lars of  at  least  one  hundred  and  thirty  have  been  com- 
puted, and  arranged  in  a  table,  for  future  comparison. 
Of  these,  six  are  particularly  remarkable ;  namely,  the 
comets  of  1680,  1770,  and  1811  ;  and  those  which  bear 
the  names  of  Halley,  Biela,  and  Encke.  The  comet 
of  1680  was  remarkable,  not  only  for  its  astonishing 
size  and  splendor,  and  its  near  approach  to  the  sun, 
but  is  celebrated  for  having  submitted  itself  to  the  ob- 
servations of  Sir  Isaac  Newton,  and  for  having  enjoy- 
ed the  signal  honor  of  being  the  first  comet  whose 
elements  were  determined  on  the  sure  basis  of  math- 
ematics. The  comet  of  1770  is  memorable  for  the 
changes  its  orbit  has  undergone  by  the  action  of  Jupi- 
ter, as  I  shall  explain  to  you  more  particularly  hereaf- 
ter. The  comet  of  1811  was  the  most  remarkable  in 
its  appearance  of  all  that  have  been  seen  in  the  present 
century.  It  had  scarcely  any  perceptible  nucleus,  but 
its  train  was  very  long  and  broad,  as  is  represented  in 
Fig.  68.  Halley's  comet  (the  same  which  reappeared 
in  1835)  is  distinguished  as  that  whose  return  was  first 
successfully  predicted,  and  whose  orbit  is  best  determin- 
ed ;  and  Biela's  and  Encke's  comets  are  well  known  for 
their  short  periods  of  revolution,  which  subject  them  fre- 
quently to  the  view  of  astronomers. 

In  magnitude  and  brightness,  comets  exhibit  great 
diversity.  History  informs  us  of  comets  so  bright,  as  to 
be  distinctly  visible  in  the  day-time,  even  at  noon,  and 
in  the  brightest  sunshine.  Such  was  the  comet  seen  at 
Rome  a  little  before  the  assassination  of  Julius  Caesar. 
The  comet  of  1680  covered  an  arc  of  the  heavens  of 


316  LETTERS  ON  ASTRONOMY. 

ninety-seven  degrees,  and  its  length  was  estimated  at 
one  hundred  and  twenty -three  millions  of  miles.  That 
of  1811  had  a  nucleus  of  only  four  hundred  and  twen- 
ty-eight miles  in  diameter,  but  a  tail  one  hundred  and 
thirty-two  millions  of  miles  long.  Had  it  been  coiled 
around  the  earth  like  a  serpent,  it  would  have  reached 
round  more  than  five  thousand  times.  Other  comets  are 
exceedingly  small,  the  nucleus  being  in  one  case  esti- 
mated at  only  twenty-five  miles ;  and  some,  which  are 
destitute  of  any  perceptible  nucleus,  appear  to  the 
largest  telescopes,  even  when  nearest  to  us,  only  as  a 
small  speck  of  fog,  or  as  a  tuft  of  down.  The  majority 
of  comets  can  be  seen  only  by  the  aid  of  the  telescope. 
Indeed,  the  same  comet  has  very  different  aspects,  at 
its  different  returns.  Halley's  comet,  in  1305,  was 
described  by  the  historians  of  that  age  as  the  comet 
of  terrific  magnitude ;  (cometa  horrendw  magnitudi- 
nis;)  in  1456  its  tail  reached  from  the  horizon  to  the 
zenith,  and  inspired  such  terror,  that,  by  a  decree  of  the 
Pope  of  Rome,  public  prayers  were  offered  up  at  noon- 
day in  all  the  Catholic  churches,  to  deprecate  the  wrath 
of  heaven  ;  while  in  1682  its  tail  was  only  thirty  de- 
grees in  length ;  and  in  1759  it  was  visible  only  to  the 
telescope  until  after  it  had  passed  its  perihelion.  At 
its  recent  return,  in  1835,  the  greatest  length  of  the  tail 
was  about  twelve  degrees.  These  changes  in  the  ap- 
pearance of  the  same  comet  are  partly  owing  to  the 
different  positions  of  the  earth  with  respect  to  them,  be- 
ing sometimes  much  nearer  to  them  when  they  cross  its 
track  than  at  others  ;  also,  one  spectator,  so  situated  as 
to  see  the  comet  at  a  higher  angle  of  elevation,  or  in  a 
purer  sky,  than  another,  will  see  the  train  longer  than 
it  appears  to  another  less  favorably  situated ;  but  the 
extent  of  the  changes  are  such  as  indicate  also  a  real 
change  in  magnitude  and  brightness. 

The  periods  of  comets  in  their  revolutions  around  the 
sun  are  equally  various.  Encke's  comet,  which  has  the 
shortest  known  period,  completes  its  revolution  in  three 
and  one  third  years ;  or,  more  accurately,  in  twelve  hun- 


COMETS.  317 

dred  and  eight  days;  while  that  of  1811  is  estimated 
to  have  a  period  of  thirty-three  hundred  and  eighty- 
three  years. 

The  distances  to  which  different  comets  recede  from 
the  sun  are  equally  various.  While  Encke's  comet  per- 
forms its  entire  revolution  within  the  orbit  of  Jupiter, 
Halley's  comet  recedes  from  the  sun  to  twice  the  dis- 
tance of  Uranus  ;  or  nearly  thirty-six  hundred  millions 
of  miles.  Some  comets,  indeed,  are  thought  to  go  a 
much  greater  distance  from  the  sun  than  this,  while 
some  are  supposed  to  pass  into  curves  which  do  not, 
like  the  ellipse,  return  into  themselves  ;  and  in  this  case 
they  never  come  back  to  the  sun.  (See  Fig.  34,  page 
153.) 

Comets  shine  by  reflecting  the  light  of  the  sun.  In 
one  or  two  instances,  they  have  been  thought  to  exhibit 
distinct  phases,  like  the  moon,  although  the  nebulous 
matter  with  which  the  nucleus  is  surrounded  would 
commonly  prevent  such  phases  from  being  distinctly 
visible,  even  when  they  would  otherwise  be  apparent. 
Moreover,  certain  qualities  of  polarized  light, — an  af- 
fection by  which  a  ray  of  light  seems  to  have  different 
properties  on  different  sides, — enable  opticians  to  decide 
whether  the  light  of  a  given  body  is  direct  or  reflected  ; 
and  M.  Arago,  of  Paris,  by  experiments  of  this  kind  on 
the  light  of  the  comet  of  1819,  ascertained  it  to  be  re- 
flected light. 

The  tail  of  a  comet  usually  increases  very  much  as 
it  approaches  the  sun ;  and  it  frequently  does  not  reach 
its  maximum  until  after  the  perihelion  passage.  In  re- 
ceding from  the  sun,  the  tail  again  contracts,  and  near- 
ly or  quite  disappears  before  the  body  of  the  comet  is 
entirely  out  of  sight.  The  tail  is  frequently  divided 
into  two  portions,  the  central  parts,  in  the  direction  of 
the  axis,  being  less  bright  than  the  marginal  parts.  In 
1744  a  comet  appeared  which  had  six  tails  spread  out 
like  a  fan. 

The  tails  of  comets  extend  in  a  direct  line  from  the 
sun,  although  more  or  less  curved,  like  a  long  quill  or 
21* 


318  LETTERS  ON  ASTRONOMY. 

feather,  being  convex  on  the  side  next  to  the  direction 
in  which  they  are  moving, — a  figure  which  may  result 
from  the  less  velocity  of  the  portion  most  remote  from 
the  sun.  Expansions  of  the  envelope  have  also  been 
at  times  observed  on  the  side  next  the  sun ;  but  these 
seldom  attain  any  considerable  length. 

The  quantity  of  matter  in  comets  is  exceedingly 
small.  Their  tails  consist  of  matter  of  such  tenuity, 
that  the  smallest  stars  are  visible  through  them.  They 
can  only  be  regarded  as  masses  of  thin  vapor,  suscepti- 
ble of  being  penetrated  through  their  whole  substance 
by  the  sunbeams,  and  reflecting  them  alike  from  their 
interior  parts  and  from  their  surfaces.  It  appears  per- 
haps incredible,  that  so  thin  a  substance  should  be  vis- 
ible by  reflected  light,  and  some  astronomers  have  held 
that  the  matter  of  comets  is  self-luminous ;  but  it  re- 
quires but  very  little  light  to  render  an  object  visible  in 
the  night,  and  a  light  vapor  may  be  visible  when  illu- 
minated throughout  an  immense  stratum,  which  could 
not  be  seen  if  spread  over  the  face  of  the  sky  like  a 
thin  cloud.  "  The  highest  clouds  that  float  in  our  at- 
mosphere," says  Sir  John  Herschel,  "  must  be  looked 
upon  as  dense  and  massive  bodies,  compared  with  the 
filmy  and  all  but  spiritual  texture  of  a  comet." 

The  small  quantity  of  matter  in  comets  is  proved  by 
the  fact,  that  they  have  at  times  passed  very  near  to  some 
of  the  planets,  without  disturbing  their  motions  in  any 
appreciable  degree.  Thus  the  comet  of  1770,  in  its  way 
to  the  sun,  got  entangled  among  the  satellites  of  Jupi- 
ter, and  remained  near  them  four  months ;  yet  it  did  not 
perceptibly  change  their  motions.  The  same  comet, 
also,  came  very  near  the  earth ;  so  that,  had  its  quan- 
tity of  matter  been  equal  to  that  of  the  earth,  it  would, 
by  its  attraction,  have  caused  the  earth  to  revolve  in  an 
orbit  so  much  larger  than  at  present,  as  to  have  in- 
creased the  length  of  the  year  two  hours  and  forty- 
seven  minutes.  Yet  it  produced  no  sensible  effect  on 
the  length  of  the  year,  and  therefore  its  mass,  as  is 
shown  by  La  Place,  could  not  have  exceeded  -^W  of 


COMETS.  319 

that  of  the  earth,  and  might  have  been  less  than  this  to 
any  extent.  It  may  indeed  be  asked,  what  proof  we 
have  that  comets  have  any  matter,  and  are  not  mere 
reflections  of  light.  The  answer  is,  that,  although  they 
are  not  able  by  their  own  force  of  attraction  to  disturb 
the  motions  of  the  planets,  yet  they  are  themselves  ex- 
ceedingly disturbed  by  the  action  of  the  planets,  and  in 
exact  conformity  with  the  laws  of  universal  gravitation. 
A  delicate  compass  may  be  greatly  agitated  by  the  vi- 
cinity of  a  mass  of  iron,  while  the  iron  is  not  sensibly 
affected  by  the  attraction  of  the  needle. 

By  approaching  very  near  to  a  large  planet,  a  comet 
may  have  its  orbit  entirely  changed.  This  fact  is  strik- 
ingly exemplified  in  the  history  of  the  comet  of  1770. 
At  its  appearance  in  1770,  its  orbit  was  found  to  be  an 
ellipse,  requiring  for  a  complete  revolution  only  five 
and  a  half  years ;  and  the  wonder  was,  that  it  had  not 
been  seen  before,  since  it  was  a  very  large  and  bright 
comet.  Astronomers  suspected  that  its  path  had  been 
changed,  and  that  it  had  been  recently  compelled  to 
move  in  this  short  ellipse,  by  the  disturbing  force  of 
Jupiter  and  his  satellites.  The  French  Institute,  there- 
fore, offered  a  high  prize  for  the  most  complete  investi- 
gation of  the  elements  of  this  comet,  taking  into  ac- 
count any  circumstances  which  could  possibly  have 
produced  an  alteration  in  its  course.  By  tracing  back 
the  movements  of  this  comet  for  some  years  previous  to 
1770,  it  was  found  that,  at  the  beginning  of  1767,  it 
had  entered  considerably  within  the  sphere  of  Jupiter's 
attraction.  Calculating  the  amount  of  this  attraction 
from  the  known  proximity  of  the  two  bodies,  it  was 
found  what  must  have  been  its  orbit  previous  to  the 
time  when  it  became  subject  to  the  disturbing  action 
of  Jupiter.  It  was  therefore  evident  why,  as  long  as  it 
continued  to  circulate  in  an  orbit  so  far  from  the  cen- 
tre of  the  system,  it  was  never  visible  from  the  earth. 
In  January,  1767,  Jupiter  and  the  comet  happened  to 
be  very  near  to  one  another,  and  as  both  were  moving 
in  the  same  direction,  and  nearly  in  the  same  plane, 


320  LETTERS  ON  ASTRONOMY. 

they  remained  in  the  neighborhood  of  each  other  for 
several  months,  the  planet  being  between  the  comet 
and  the  sun.  The  consequence  was,  that  the  comet's 
orbit  was  changed  into  a  smaller  ellipse,  in  which  its 
revolution  was  accomplished  in  five  and  a  half  years. 
But  as  it  approached  the  sun,  in  1779,  it  happened 
again  to  fall  in  with  Jupiter.  It  was  in  the  month  of 
June  that  the  attraction  of  the  planet  began  to  have  a 
sensible  effect ;  and  it  was  not  until  the  month  of  Oc- 
tober following,  that  they  were  finally  separated. 

At  the  time  of  their  nearest  approach,  in  August, 
Jupiter  was  distant  from  the  comet  only  ^T  of  its  dis- 
tance from  the  sun,  and  exerted  an  attraction  upon  it 
two  hundred  and  twenty-five  times  greater  than  that  of 
the  sun.  By  reason  of  this  powerful  attraction,  Jupi- 
ter being  further  from  the  sun  than  the  comet,  the  lat- 
ter was  drawn  out  into  a  new  orbit,  which  even  at  its 
perihelion  came  no  nearer  to  the  sun  than  the  planet 
Ceres.  In  this  third  orbit,  the  comet  requires  about 
twenty  years  to  accomplish  its  revolution  ;  and  being  at 
so  great  a  distance  from  the  earth,  it  is  invisible,  and 
will  for  ever  remain  so,  unless,  in  the  course  of  ages,  it 
may  undergo  new  perturbations,  and  move  again  in 
some  smaller  orbit,  as  before. 

With  the  foregoing  leading  facts  respecting  comets 
in  view,  I  will  now  explain  to  you  a  few  things  equally 
remarkable  respecting  their  motions. 

The  paths  of  the  planets  around  the  sun  being  near- 
ly circular,  we  are  able  to  see  a  planet  in  every  part  of 
its  orbit.  But  the  case  is  very  different  with  comets. 
For  the  greater  part  of  their  course,  they  are  wholly 
out  of  sight,  and  come  into  view  only  while  just  in  the 
neighborhood  of  the  sun.  This  you  will  readily  see 
must  be  the  case,  by  inspecting  the  frontispiece, 
which  represents  the  orbit  of  Biela's  comet,  in  1832. 
Sometimes,  the  orbit  is  so  eccentric,  that  the  place 
of  the  focus  occupied  by  the  sun  appears  almost  at 
the  extremity  of  the  orbit.  This  was  the  case  with  the 
orbit  of  the  comet  of  1680.  Indeed,  this  comet,  at 


COMETS.  321 

its  perihelion,  came  in  fact  nearer  to  the  sun  than  the 
sixth  part  of  the  sun's  diameter,  being  only  one  hun- 
dred and  forty-six  thousand  miles  from  the  surface  of  the 
sun,  which,  you  will  remark,  is  only  a  little  more  than  half 
the  distance  of  the  moon  from  the  earth ;  while,  at  its 
aphelion,  it  was  estimated  to  be  thirteen  thousand  mil- 
lions of  miles  from  the  sun, — more  than  eleven  thousand 
millions  of  miles  beyond  the  planet  Uranus.  Its  veloci- 
ty, when  nearest  the  sun,  exceeded  a  million  of  miles  an 
hour.  To  describe  such  an  orbit  as  was  assigned  to  it 
by  Sir  Isaac  Newton,  would  require  five  hundred  and 
seventy-five  years.  During  all  this  period,  it  was  entire- 
ly out  of  view  to  the  inhabitants  of  the  earth,  except  the 
few  months,  while  it  was  running  down  to  the  sun  from 
such  a  distance  as  the  orbit  of  Jupiter  and  back.  The 
velocity  of  bodies  moving  in  such  eccentric  orbits  dif- 
fers widely  in  different  parts  of  their  orbits.  In  the 
remotest  parts  it  is  so  slow,  that  years  would  be  requir- 
ed to  pass  over  a  space  equal  to  that  which  it  would 
run  over  in  a  single  day,  when  near  the  sun. 

The  appearances  of  the  same  comet  at  different  pe- 
riods of  its  return  are  so  various,  that  we  can  never 
pronounce  a  given  comet  to  be  the  same  with  one  that 
has  appeared  before,  from  any  peculiarities  in  its  phys- 
ical aspect,  as  from  its  color,  magnitude,  or  shape  ;  since, 
in  all  these  respects,  it  is  very  different  at  different  re- 
turns ;  but  it  is  judged  to  be  the  same  if  its  path  through 
the  heavens,  as  traced  among  the  stars,  is  the  same. 

The  comet  whose  history  is  the  most  interesting,  and 
which  both  of  us  have  been  privileged  to  see,  is  Hal- 
ley's.  Just  before  its  latest  visit,  in  1835,  its  return 
was  anticipated  with  so  much  expectation,  not  only 
by  astronomers,  but  by  all  classes  of  the  community, 
that  a  great  and  laudable  eagerness  universally  prevail- 
ed, to  learn  the  particulars  of  its  history.  The  best 
summary  of  these,  which  I  met  with,  was  given  in  the 
Edinburgh  Review  for  April,  1835.  I  might  content 
myself  with  barely  referring  you  to  that  well-written  ar- 
ticle ;  but,  as  you  may  not  have  the  work  at  hand,  and 


322  LETTERS  ON  ASTRONOMY. 

would,  moreover,  probably  not  desire  to  read  the  whole 
article,  I  will  abridge  it  for  your  perusal,  interspersing 
some  remarks  of  my  own.  I  have  desired  to  give  you, 
in  the  course  of  these  Letters,  some  specimen  of  the 
labors  of  astronomers,  and  shall  probably  never  be  able 
to  find  a  better  one. 

It  is  believed  that  the  first  recorded  appearance  of 
Halley's  comet  was  that  which  was  supposed  to  sig- 
nalize the  birth  of  Mithridates,  one  hundred  and  thirty 
years  before  the  birth  of  Christ.  It  is  said  to  have 
appeared  for  twenty-four  days ;  its  light  is  said  to 
have  surpassed  that  of  the  sun ;  its  magnitude  to  have 
extended  over  a  fourth  part  of  the  firmament ;  and  it 
is  stated  to  have  occupied,  consequently,  about  four 
hours  in  rising  and  setting.  In  the  year  323,  a  comet 
appeared  in  the  sign  Virgo.  Another,  according  to 
the  historians  of  the  Lower  Empire,  appeared  in  the 
year  399,  seventy-six  years  after  the  last,  at  an  interval 
corresponding  to  that  of  Halley's  comet.  The  interval 
between  the  birth  of  Mithridates  and  the  year  323 
was  four  hundred  and  fifty-three  years,  which  would 
be  equivalent  to  six  periods  of  seventy-five  and  a  half 
years.  Thus  it  would  seem,  that  in  the  interim  there 
were  five  returns  of  this  comet  unobserved,  or  at  least 
unrecorded.  The  appearance  in  the  year  399  was  at- 
tended with  extraordinary  circumstances.  It  was  de- 
scribed in  the  old  writers  as  a  "  comet  of  monstrous  size 
and  appalling  aspect,  its  tail  seeming  to  reach  down  to 
the  ground."  The  next  recorded  appearance  of  a  com- 
et agreeing  with  the  ascertained  period  marks  the  tak- 
ing of  Rome,  in  the  year  550, — an  interval  of  one  hun- 
dred and  fifty-one  years,  or  two  periods  of  seventy-five 
and  a  half  years  having  elapsed.  One  unrecorded  return 
must,  therefore,  have  taken  place  in  the  interim.  The 
next  appearance  of  a  comet,  coinciding  with  the  assigned 
period,  is  three  hundred  and  eighty  years  afterwards ; 
namely,  in  the  year  930, — five  revolutions  having  been 
completed  in  the  interval.  The  next  appearance  is  re- 
corded in  the  year  1005,  after  an  interval  of  a  single 


COMETS.  323 

period  of  seventy-five  years.  Three  revolutions  would 
now  seem  to  have  passed  unrecorded,  when  the  comet 
again  makes  its  appearance  in  1230.  In  this,  as  well 
as  in  former  appearances,  it  is  proper  to  state,  that  the 
sole  test  of  identity  of  these  comets  with  that  of  Halley 
is  the  coincidence  of  the  times,  as  near  as  historical 
records  enable  us  to  ascertain,  with  the  epochs  at 
which  the  comet  of  Halley  might  be  expected  to  ap- 
pear. That  such  evidence,  however,  is  very  imperfect, 
must  be  evident,  if  the  frequency  of  cometary  appear- 
ances be  considered,  and  if  it  be  remembered,  that  hith- 
erto we  find  no  recorded  observations,  which  could 
enable  us  to  trace,  even  with  the  rudest  degree  of 
approximation,  the  paths  of  those  comets,  the  times  of 
whose  appearances  raise  a  presumption  of  their  identi- 
ty with  that  of  Halley.  We  now,  however,  descend  to 
times  in  which  more  satisfactory  evidence  may  be  ex- 
pected. 

In  the  year  1305,  a  year  in  which  the  return  of  Hal- 
ley's  comet  might  have  been  expected,  there  is  record- 
ed a  comet  of  remarkable  character :  "  A  comet  of  ter- 
rific dimensions  made  its  appearance  about  the  time 
of  the  feast  of  the  Passover,  which  was  followed  by  a 
Great  Plague."  Had  the  terrific  appearance  of  this 
body  alone  been  recorded,  this  description  might  have 
passed  without  the  charge  of  great  exaggeration  ;  but 
when  we  find  the  Great  Plague  connected  with  it  as  a 
consequence,  it  is  impossible  not  to  conclude,  that  the 
comet  was  seen  by  its  historians  through  the  magnify- 
ing medium  of  the  calamity  which  followed  it.  Anoth- 
er appearance  is  recorded  in  the  year  1380,  unaccom- 
panied by  any  other  circumstance  than  its  mere  date. 
This,  however,  is  in  strict  accordance  with  the  ascer- 
tained period  of  Halley's  comet. 

We  now  arrive  at  the  first  appearance  at  which  ob- 
servations were  taken,  possessing  sufficient  accuracy  to 
enable  subsequent  investigators  to  determine  the  path 
of  the  comet ;  and  this  is  accordingly  the  first  comet 
the  identity  of  which  with  the  comet  of  Halley  can 


324  LETTERS  ON  ASTRONOMY. 

be  said  to  be  conclusively  established.  In  the  year 
1456,  a  comet  is  stated  to  have  appeared  "  of  unheard 
of  magnitude  ;"  it  was  accompanied  by  a  tail  of  extra- 
ordinary length,  which  extended  over  sixty  degrees,  (a 
third  part  of  the  heavens,)  and  continued  to  be  seen 
during  the  whole  month  of  June.  The  influence  which 
was  attributed  to  this  appearance  renders  it  probable, 
that  in  the  record  there  is  more  or  less  of  exaggeration. 
It  was  considered  as  the  celestial  indication  of  the  rap- 
id success  of  Mohammed  the  Second,  who  had  taken 
Constantinople,  and  struck  terror  into  the  whole  Chris- 
tian world.  Pope  Calixtus  the  Second  levelled  the 
thunders  of  the  Church  against  the  enemies  of  his 
faith,  terrestrial  and  celestial ;  and  in  the  same  Bull  ex- 
communicated the  Turks  and  the  comet ;  and,  in  order 
that  the  memory  of  this  manifestation  of  his  power 
should  be  for  ever  preserved,  he  ordained  that  the  bells 
of  all  the  churches  should  be  rung  at  mid-day, — a  cus- 
tom which  is  preserved  in  those  countries  to  our  times. 

The  extraordinary  length  and  brilliancy  which  was 
ascribed  to  the  tail,  upon  this  occasion,  have  led  astron- 
omers to  investigate  the  circumstances  under  which  its 
brightness  and  magnitude  would  be  the  greatest  possi- 
ble ;  and  upon  tracing  back  the  motion  of  the  comet  to 
the  year  1456,  it  has  been  found  that  it  was  then  ac- 
tually in  the  position,  with  respect  to  the  earth  and  sun, 
most  favorable  to  magnitude  and  splendor.  So  far, 
therefore,  the  result  of  astronomical  calculation  corrob- 
orates the  records  of  history. 

The  next  return  took  place  in  1531.  Pierre  Appi- 
an,  who  first  ascertained  the  fact  that  the  tails  of  comets 
are  usually  turned  from  the  sun,  examined  this  comet 
with  a  view  to  verify  his  statement,  and  to  ascertain  the 
true  direction  of  its  tail.  He  made,  accordingly,  nu- 
merous observations  upon  its  position,  which,  although 
rude,  compared  with  the  present  standard  of  accuracy, 
were  still  sufficiently  exact  to  enable  Halley  to  identify 
this  comet  with  that  observed  by  himself. 

The  next  return  took  place  in  1607,  when  the  comet 


COMETS*  325 

Was  observed  by  Kepler.  This  astronomer  first  saw  it 
on  the  evening  of  the  twenty-sixth  of  September,  when 
it  had  the  appearance  of  a  star  of  the  first  magnitude, 
and,  to  his  vision,  was  without  a  tail ;  but  the  friends 
who  accompanied  him  had  better  sight,  and  distinguish- 
ed the  tail.  Before  three  o'clock  the  following  morning 
the  tail  had  become  clearly  visible,  and  had  acquired 
great  magnitude.  Two  days  afterwards,  the  comet 
was  observed  by  Longomontanus,  a  distinguished  phi- 
losopher of  the  time.  He  describes  its  appearance,  to 
the  naked  eye,  to  be  like  Jupiter,  but  of  a  paler  and 
more  obscured  light ;  that  its  tail  was  of  considerable 
length,  of  a  paler  light  than  that  of  the  head,  and  more 
dense  than  the  tails  of  ordinary  comets. 

The  next  appearance,  and  that  which  was  observed 
by  Halley  himself,  took  place  in  1682,  a  little  before 
the  publication  of  the  '  Principia.'  In  the  interval 
between  1607  and  1682,  practical  astronomy  had  made 
great  advances ;  instruments  of  observation  had  been 
brought  to  a  state  of  comparative  perfection  ;  numer- 
ous observatories  had  been  established,  and  the  man- 
agement of  them  had  been  confided  to  the  most  emi- 
nent men  in  Europe.  In  1682,  the  scientific  world 
was  therefore  prepared  to  examine  the  visitor  of  our 
system  with  a  degree  of  care  and  accuracy  before  un- 
known. 

In  the  year  1686,  about  four  years  afterwards,  New- 
ton published  his  '  Principia,'  in  which  he  applied  to 
the  comet  of  1680  the  general  principles  of  physical 
investigation  first  promulgated  in  that  work.  He  ex- 
plained the  method  of  determining,  by  geometrical 
construction,  the  visible  portion  of  the  path  of  a  body 
of  this  kind,  and  invited  astronomers  to  apply  these 
principles  to  the  various  recorded  comets, — to  discover 
whether  some  among  them  might  not  have  appeared 
at  different  epochs,  the  future  returns  of  which  might 
consequently  be  predicted.  Such  was  the  effect  of  the 
force  of  analogy  upon  the  mind  of  Newton,  that,  with- 
out awaiting  the  discovery  of  a  periodic  comet,  he  bold- 

28  L.  A. 


LETTERS  ON  ASTRONOMY. 

ly  assumed  these  bodies  to  be  analogous  to  planets  in 
their  revolution  round  the  sun. 

Extraordinary  as  these  conjectures  must  have  appear- 
ed at  the  time,  they  were  soon  strictly  realized.  Hal- 
ley,  who  was  then  a  young  man,  but  possessed  one  of 
the  best  minds  in  England,  undertook  the  labor  of  ex- 
amining the  circumstances  attending  all  the  comets 
previously  recorded,  with  a  view  to  discover  whether 
any,  and  which  of  them,  appeared  to  follow  the  same 
path.  Antecedently  to  the  year  1700,  four  hundred 
and  twenty-five  of  these  bodies  had  been  recorded  in 
history  ;  but  those  which  had  appeared  before  the  four- 
teenth century  had  not  been  submitted  to  any  observa- 
tions by  which  their  paths  could  be  ascertained, — at 
least,  not  with  a  sufficient  degree  of  precision,  to  afford 
any  hope  of  identifying  them  with  those  of  other  com- 
ets. Subsequently  to  the  year  1300,  however,  Halley 
found  twenty-four  comets  on  which  observations  had 
been  made  and  recorded,  with  a  degree  of  precision 
sufficient  to  enable  him  to  calculate  the  actual  paths 
which  these  bodies  followed  while  they  were  visible. 
He  examined,  with  the  most  elaborate  care,  the  courses 
of  each  of  these  twenty-four  bodies ;  he  found  the  ex- 
act points  at  which  each  one  of  them  crossed  the  eclip- 
tic, or  their  nodes ;  also  the  angle  which  the  direction 
of  their  motion  made  with  that  plane, — that  is,  the  in- 
clination of  their  orbits ;  he  also  calculated  the  nearest 
distance  at  which  each  of  them  approached  the  sun,  or 
their  perihelion  distance ;  and  the  exact  place  of  the 
body  when  at  that  nearest  point, — that  is,  the  longi- 
tude of  the  perihelion.  These  particulars  are  called 
the  elements  of  a  comet,  because,  when  ascertained, 
they  afford  sufficient  data  for  determining  a  comet's 
path.  On  comparing  these  paths,  Halley  found  that 
one,  which  had  appeared  in  1661,  followed  nearly  the 
same  path  as  one  which  had  appeared  in  1532.  Sup- 
posing, then,  these  to  be  two  successive  appearances  of 
the  same  comet,  it  would  follow,  that  its  period  would 
be  one  hundred  and  twenty-nine  years,  reckoning  from 


COMETS. 


327 


1661.  Had  this  conjecture  been  well  founded,  the 
comet  must  have  appeared  about  the  year  1790.  No 
comet,  however,  appeared  at  or  near  that  time,  follow- 
ing a  similar  path. 

In  his  second  conjecture,  Halley  was  more  fortunate, 
as  indeed  might  be  expected,  since  it  was  formed  upon 
more  conclusive  grounds.  He  found  that  the  paths  of 
comets  which  had  appeared  in  1531  and  1607  were 
nearly  identical,  and  that  tha^were  in  fact  the  same  as 
the  path  followed  by  the  comet  observed  by  himself  in 
168-2.  He  suspected,  therefore,  that  the  appearances  at 
these  three  epochs  were  produced  by  three  successive 
returns  of  the  same  comet,  and  that,  consequently,  its 
period  in  its  orbit  must  be  about  seventy-five  and  a 
half  years.  The  probability  of  this  conclusion  is  strik- 
ingly exhibited  to  the  eye,  by  presenting  the  elements 
in  a  tabular  form,  from  which  it  will  at  once  be  seen 
how  nearly  they  correspond  at  these  regular  intervals. 


Time. 

Inclination  of 
the  orbit. 

Long,  of  the 
node. 

Long.  Per. 

Per.  Dist. 

Course. 

1456 
1531 
1607 
1682 

17°56' 
17  56 
17  02 
17  42 

48°30' 
49  25 
50  21 

50  48 

301°00' 
301  39 
302  16 
301  36 

0°58' 
0  57 

0  58 
0  58 

Retrograde. 
ft 

1  1 

So  little  was  the  scientific  world,  at  this  time,  pre- 
pared for  such  an  announcement,  that  Halley  himself 
only  ventured  at  first  to  express  his  opinion  in  the  form 
of  conjecture ;  but,  after  some  further  investigation  of 
the  circumstances  of  the  recorded  comets,  he  found 
three  which,  at  least  in  point  of  time,  agreed  with  the 
period  assigned  to  the  comet  of  1682.  Collecting  con- 
fidence from  these  circumstances,  he  announced  his 
discovery  as  the  result  of  observation  and  calculation 
combined,  and  entitled  to  as  much  confidence  as  any 
other  consequence  of  an  established  physical  law. 

There  were,  nevertheless,  two  circumstances  which 
might  be  supposed  to  offer  some  difficulty.  First,  the 
intervals  between  the  supposed  successive  returns  were 
not  precisely  equal ;  and,  secondly,  the  inclination  of 


328  LETTERS  ON  ASTRONOMY. 

the  comet's  path  to  the  plane  of  the  earth's  orbit  was 
not  exactly  the  same  in  each  case.  Halley,  however, 
with  a  degree  of  sagacity  which,  considering  the  state 
of  knowledge  at  the  time,  cannot  fail  to  excite  unqual- 
ified admiration,  observed,  that  it  was  natural  to  sup- 
pose that  the  same  causes  which  disturbed  the  planeta- 
ry motions  must  likewise  act  upon  comets ;  and  that 
their  influence  would  be  so  much  the  more  sensible 
upon  these  bodies,  becsfltee  of  their  great  distances 
from  the  sun.  Thus,  as  the  attraction  of  Jupiter  for 
Saturn  was  known  to  affect  the  velocity  of  the  latter 
planet,  sometimes  retarding  and  sometimes  accelerating 
it,  according  to  their  relative  position,  so  as  to  affect  its 
period  to  the  extent  of  thirteen  days,  it  might  well  be 
supposed,  that  the  comet  might  suffer  by  a  similar  at- 
traction an  effect  sufficiently  great,  to  account  for  the 
inequality  observed  in  the  interval  between  its  succes- 
sive returns :  and  also  for  the  variation  to  which  the 
direction  of  its  path  upon  the  plane  of  the  ecliptic  was 
found  to  be  subject.  He  observed,  in  fine,  that,  as  in 
the  interval  between  1607  and  1682,  the  comet  passed 
so  near  Jupiter  that  its  velocity  must  have  been  aug- 
mented, and  consequently  its  period  shortened,  by  the 
action  of  that  planet,  this  period,  therefore,  having  been 
only  seventy-five  years,  he  inferred  that  the  following 
period  would  probably  be  seventy-six  years,  or  upwards ; 
and  consequently,  that  the  comet  ought  not  to  be  ex- 
pected to  appear  until  the  end  of  1758,  or  the  begin- 
ning of  1759.  It  is  impossible  to  imagine  any  quality 
of  mind  more  enviable  than  that  which,  in  the  existing 
state  of  mathematical  physics,  could  have  led  to  such 
a  prediction.  The  imperfect  state  of  mathematical 
science  rendered  it  impossible  for  Halley  to  offer  to  the 
world  a  demonstration  of  the  event  which  he  foretold. 
The  theory  of  gravitation,  which  was  in  its  infancy  in 
the  time  of  Halley's  investigations,  had  grown  to  com- 
parative maturity  before  the  period  at  which  his  pre- 
diction could  be  fulfilled.  The  exigencies  of  that  the- 
ory gave  birth  to  new  and  more  powerful  instruments 


COMETS.  329 

of  mathematical  inquiry:  the  differential  and  integral 
calculus,  or  the  science  of  fluxions,  as  it  is  sometimes 
called, — -a  branch  of  the  mathematics,  expressed  by  al- 
gebraic symbols,  but  capable  of  a  much  higher  reach, 
as  an  instrument  of  investigation,  than  either  algebra 
or  geometry, — was  its  first  and  greatest  offspring.  This 
branch  of  science  was  cultivated  with  an  ardor  and 
success  by  which  it  was  enabled  to  answer  all  the  de- 
mands of  physics,  and  it  corrffibuted  largely  to  the  ad- 
vancement of  mechanical  science  itself,  building  upon 
the  laws  of  motion  a  structure  which  has  since  been 
denominated  '  Celestial  Mechanics.'  Newton's  discov- 
eries having  obtained  reception  throughout  the  scientific 
world,  his  inquiries  and  his  theories  were  followed  up ; 
and  the  consequences  of  the  great  principle  of  univer- 
sal gravitation  were  rapidly  developed.  Since,  accord- 
ing to  this  doctrine,  every  body  in  nature  attracts  and 
is  attracted  by  every  other  body,  it  follows,  that  the 
comet  was  liable  to  be  acted  on  by  each  of  the  planets, 
as  well  as  by  the  sun, — a  circumstance  which  rendered 
its  movements  much  more  difficult  to  follow,  than  would 
be  the  case  were  it  subject  merely  to  the  projectile  force 
and  to  the  solar  attraction.  To  estimate  the  time  it 
would  take  for  a  ship  to  cross  the  Atlantic  would  be 
an  easy  task,  were  she  subject  to  only  one  constant 
wind ;  but  to  estimate,  beforehand,  the  exact  influence 
which  all  other  winds  and  the  tides  might  have  upon 
her  passage,  some  accelerating  and  some  retarding  her 
course,  would  present  a  problem  of  the  greatest  diffi- 
culty. Clairaut,  however,  a  celebrated  French  mathe- 
matician, undertook  to  estimate  the  effects  that  would 
be  produced  on  Halley's  comet  by  the  attractions  of  all 
the  planets.  His  aim  was  to  investigate  general  rules, 
by  which  the  computation  could  be  made  arithmetical- 
ly, and  hand  them  over  to  the  practical  calculator,  to 
make  the  actual  computations.  Lalande,  a  practical 
astronomer,  no  less  eminent  in  his  own  department, 
and  who  indeed  first  urged  Clairaut  to  this  inquiry, 
undertook  the  management  of  the  astronomical  and 


330  LETTERS  ON  ASTRONOMY. 

arithmetical  part  of  the  calculation.  In  this  prodigious 
labor  (for  it  was  one  of  most  appalling  magnitude)  he 
was  assisted  by  the  wife  of  an  eminent  watchmaker  in 
Paris,  named  Lepaute,  whose  exertions  on'  this  occasion 
have  deservedly -registered  her  name  in  astronomical 
history. 

It  is  difficult  to  convey  to  one  who  is  not  convers- 
ant with  such  investigations,  an  adequate  notion  of 
the  labor  which  such  an  inquiry  involved.  The  calcu- 
lation of  the  influence  of  any  one  planet  of  the  system 
upon  any  other  is  itself  a  problem  of  some  complexity 
and  difficulty ;  but  still,  one  general  computation,  de- 
pending upon  the  calculation  of  the  terms  of  a  certain 
series,  is  sufficient  for  its  solution.  This  comparative 
simplicity  arises  entirely  from  two  circumstances  which 
characterize  the  planetary  orbits.  These  are,  that, 
though  they  are  ellipses,  they  differ  very  slightly  from 
circles ;  and  though  the  planets  do  not  move  in  the 
plane  of  the  ecliptic,  yet  none  of  them  deviate  consid- 
erably from  that  plane.  But  these  characters  do  not 
belong  to  the  orbits  of  comets,  which,  on  the  contrary, 
are  highly  eccentric,  and  make  all  possible  angles  with 
the  ecliptic.  The  consequence  of  this  is,  that  the  cal- 
culation of  the  disturbances  produced  in  the  cometary 
orbits  by  the  action  of  the  planets  must  be  conducted, 
not  like  the  planets,  in  one  general  calculation  applica- 
ble to  the  whole  orbits,  but  in  a  vast  number  of  separ- 
ate calculations  ;  in  which  the  orbit  is  considered,  as  it 
were,  bit  by  bit,  each  bit  requiring  a  calculation  similar 
to  the  whole  orbit  of  the  planet.  Now,  when  it  is 
considered  that  the  period  of  Halley's  comet  is  about 
seventy-five  years,  and  that  every  portion  of  its  course, 
for  two  successive  periods,  was  necessary  to  be  calcu- 
lated separately  in  this  way,  some  notion  may  be  formed 
of  the  labor  encountered  by  Lalande  and  Madame  Le- 
paute.  "  During  six  months,"  says  Lalande,  "  we  cal- 
culated from  morning  till  night,  sometimes  even  at 
meals ;  the  consequence  of  which  was,  that  I  contract- 
ed an  illness  which  changed  my  constitution  for  the 


COMETS.  331 

remainder  of  my  life.  The  assistance  rendered  by 
Madame  Lepaute  was  such,  that,  without  her,  we  never 
could  have  dared  to  undertake  this  enormous  labor,  in 
which  it  was  necessary  to  calculate  the  distance  of  each 
of  the  two  planets,  Jupiter  and  Saturn,  from  the  com- 
et, and  their  attraction  upon  that  body,  separately,  for 
every  successive  degree,  and  for  one  hundred  and  fifty 
years." 

The  attraction  of  a  body  is  proportioned  to  its  quan- 
tity of  matter.  Therefore,  before  the  attraction  exert- 
ed upon  the  comet,  by  the  several  planets  within  whose 
influence  it  might  fall,  could  be  correctly  estimated,  it 
was  necessary  to  know  the  mass  of  each  planet ;  and 
though  the  planets  had  severally  been  weighed  by 
methods  supplied  by  Newton's  '  Principia,'  yet  the  es- 
timate had  not  then  attained  the  same  measure  of  ac- 
curacy as  it  has  now  reached ;  nor  was  it  certain  that 
there  was  not  (as  it  has  since  appeared  that  there  ac- 
tually was)  one  or  more  planets  beyond  Saturn,  whose 
attractions  might  likewise  influence  the  motions  of  the 
comet.  Clairaut,  making  the  best  estimate  he  was 
able,  under  all  these  disadvantages,  of  the  disturbing 
influence  of  the  planets,  fixed  the  return  of  the  comet 
to  the  place  of  its  nearest  distance  from  the  sun  on  the 
fourth  of  April,  1759. 

In  the  successive  appearances  of  the  comet,  subse- 
quently to  1456,  it  was  found  to  have  gradually  decreas- 
ed in  magnitude  and  splendor.  While  in  1456  it 
reached  across  one  third  part  of  the  firmament,  and 
spread  terror  over  Europe,  in  1607,  its  appearance, 
when  observed  by  Kepler  and  Longomontanus,  was  that 
of  a  star  of  the  first  magnitude  ;  and  so  trifling  was  its 
tail  that,  Kepler  himself,  when  he  first  saw  it,  doubted 
whether  it  had  any.  In  1682,  it  excited  little  attention, 
except  among  astronomers.  Supposing  this  decrease 
of  magnitude  and  brilliancy  to  be  progressive,  Lalande 
entertained  serious  apprehensions  that  on  its  expected 
return  it  might  be  so  inconsiderable,  as  to  escape  the 
observation  even  of  astronomers ;  and  thus,  that  this 


33£  LETTERS  ON  ASTRONOMY. 

splendid  example  of  the  power  of  science,  and  unan- 
swerable proof  of  the  principle  of  gravitation,  would 
be  lost  to  the  world. 

It  is  not  uninteresting  to  observe  the  misgivings  of 
this  distinguished  astronomer  with  respect  to  the  ap- 
pearance of  the  body,  mixed  up  with  his  unshaken 
faith  in  the  result  of  the  astronomical  inquiry.  "  We 
cannot  doubt,"  says  he,  "  that  it  will  return  ;  and  even 
if  astronomers  cannot  see  it,  they  will  not  therefore  be 
the  less  convinced  of  its  presence.  They  know  that 
the  faintness  of  its  light,  its  great  distance,  and  perhaps 
even  bad  weather,  may  keep  it  from  our  view.  But  the 
world  will  find  it  difficult  to  believe  us  ;  they  will  place 
this  discovery,  which  has  done  so  much  honor  to  mod- 
ern philosophy,  among  the  number  of  chance  predic- 
tions. We  shall  see  discussions  spring  up  again  in 
colleges,  contempt  among  the  ignorant,  terror  among 
the  people  ;  and  seventy-six  years  will  roll  away,  be- 
fore there  will  be  another  opportunity  of  removing  all 
doubt." 

Fortunately  for  science,  the  arrival  of  the  expected 
visitor  did  not  take  place  under  such  untoward  circum- 
stances. As  the  commencement  of  the  year  1759  ap- 
proached, "  astronomers,"  says  Voltaire,  "  hardly  went 
to  bed  at  all."  The  honor,  however,  of  the  first  glimpse 
of  the  stranger  was  not  reserved  for  the  possessors 
of  scientific  rank,  nor  for  the  members  of  academies 
or  universities.  On  the  night  of  Christmas-day,  1758, 
George  Palitzch,  of  Politz,  near  Dresden, — "  a  peasant," 
says  Sir  John  Herchel,  "  by  station,  an  astronomer  by 
nature,"  first  saw  the  comet. 

An  astronomer  of  Leipzic  found  it  soon  after ;  but, 
with  the  mean  jealousy  of  a  miser,  he  concealed  his 
treasure,  while  his  contemporaries  throughout  Europe 
were  vainly  directing  their  anxious  search  after  it  to 
other  quarters  of  the  heavens.  At  this  time,  Delisle, 
a  French  astronomer,  and  his  assistant,  Messier,  who, 
from  his  unweared  assiduity  in  the  pursuit  of  comets, 
was  called  the  Comet-Hunter,  had  been  constantly 


COMETS.  333 

engaged,  for  eighteen  months,  in  watching  for  the  re- 
turn of  Halley's  comet.  Messier  passed  his  life  in 
search  of  comets.  It  is  related  of  him,  that  when  he 
was  in  expectation  of  discovering  a  comet,  his  wife  was 
taken  ill  and  died.  While  attending  on  her,  being 
withdrawn  from  his  observatory,  another  astronomer 
anticipated  him  in  the  discovery.  Messier  was  in  des- 
pair. A  friend,  visiting  him,  began  to  offer  some  con- 
solation for  the  recent  affliction  he  had  suffered.  Mes- 
sier, thinking  only  of  the  comet,  exclaimed,  "  I  had  dis- 
covered twelve :  alas,  that  I  should  be  robbed  of  the 
thirteenth  by  Montagne !" — and  his  eyes  filled  with 
tears.  Then,  remembering  that  it  was  necessary  to 
mourn  for  his  wife,  whose  remains  were  still  in  the 
house,  he  exclaimed,  "  Ah  !  this  poor  woman  !"  (ah  I 
cette  pauvre  femme,)  and  again  wept  for  his  comet. 
We  can  easily  imagine  how  eagerly  such  an  enthusiast 
would  watch  for  Halley's  comet ;  and  we  could  almost 
wish  that  it  had  been  his  good  fortune  to  be  the  first 
to  announce  its  arrival ;  but,  being  misled  by  a  chart 
which  directed  his  attention  to  the  wrong  part  of  the 
firmament,  a  whole  month  elapsed  after  its  discovery 
by  Palitzch,  before  he  enjoyed  the  delightful  spectacle. 
The  comet  arrived  at  its  perihelion  on  the  thirteenth 
of  March,  only  twenty-three  days  from  the  time  assign- 
ed by  Clairaut.  It  appeared  very  round,  with  a  bril- 
liant nucleus,  well  distinguished  from  the  surrounding 
nebulosity.  It  had,  however,  no  appearance  of  a  tail. 
It  became  lost  in  the  sun,  as  it  approached  its  perihe- 
lion, and  emerged  again,  on  the  other  side  of  the  sun, 
on  the  first  of  April.  Its  exhibiting  an  appearance,  so 
inferior  to  what  it  presented  on  some  of  its  previous  re- 
turns, is  partly  accounted  for  by  its  being  seen  by  the 
European  astronomers  under  peculiarly  disadvantageous 
circumstances,  being  almost  always  within  the  twilight, 
and  in  the  most  unfavorable  situations.  In  the  south- 
ern hemisphere,  however,  the  circumstances  for  observ- 
ing it  were  more  favorable,  and  there  it  exhibited  a  tail 
varying  from  ten  to  forty-seven  degrees  in  length,- 


334  LETTERS  ON  ASTRONOMY. 

In  my  next  Letter  I  will  give  you  some  particulars 
respecting  the  late  return  of  Halley's  comet. 


LETTER  XXVI. 

COMETS,   CONTINUED. 

"  Incensed  with  indignation,  Satan  stood 
Unterrifled,  and  like  a  comet  burned, 
That  fires  the  length  of  Ophiucus  huge 
In  the  Arctic  sky,  and  from  his  horrid  train 
Shakes  pestilence  and  war." — Milton. 

AMONG  other  great  results  which  have  marked  the 
history  of  Halley's  comet,  it  has  itself  been  a  criterion 
of  the  existing  state  of  the  mathematical  and  astronom- 
ical sciences.  We  have  just  seen  how  far  the  knowl- 
edge of  the  great  laws  of  physical  astronomy,  and  of 
the  higher  mathematics,  enabled  the  astronomers  of 
1682  and  1759,  respectively,  to  deal  with  this  wonder- 
ful body ;  and  let  us  now  see  what  higher  advantages 
were  possessed  by  the  astronomers  of  1835.  During 
this  last  interval  of  seventy-six  years,  the  science  of 
mathematics,  in  its  most  profound  and  refined  branch- 
es, has  made  prodigious  advances,  more  especially  in 
its  application  to  the  laws  of  the  celestial  motions,  as 
exemplified  in  the  c  Mecanique  Celeste'  of  La  Place. 
The  methods  of  investigation  have  acquired  greater 
simplicity,  and  have  likewise  become  more  general  and 
comprehensive ;  and  mechanical  science,  in  the  largest 
sense  of  that  term,  now  embraces  in  its  formularies  the 
most  complicated  motions,  and  the  most  minute  effects 
of  the  mutual  influences  of  the  various  members  of  our 
system.  You  will  probably  find  it  difficult  to  compre- 
hend, how  such  hidden  facts  can  be  disclosed  by  for- 
mularies, consisting  of  a's  and  6's,  and  x's  and  i/'s,  and 
other  algebraic  symbols  ;  nor  will  it  be  easy  to  give 
you  a  clear  idea  of  this  subject,  without  a  more  exten- 
sive acquaintance  than  you  have  formed  with  algebraic 
investigations ;  but  you  can  easily  understand  that  even 


COMETS.  335 

an  equation  expressed  in  numbers  may  be  so  changed  in 
its  form,  by  adding,  subtracting,  multiplying  and  divid- 
ing, as  to  express  some  new  truth  at  every  transforma- 
tion. Some  idea  of  this  may  be  formed  by  the  sim- 
plest example.  Take  the  following:  3+4=7.  This 
equation  expresses  the  fact,  that  three  added  to  four  is 
equal  to  seven.  By  multiplying  all  the  terms  by  2,  we 
obtain  a  new  equation,  in  which  6+8=14.  This  ex- 
presses a  new  truth ;  and  by  varying  the  form,  by  sim- 
ilar operations,  an  indefinite  number  of  separate  truths 
may  be  elicited  from  the  simple  fundamental  expres- 
sion. I  will  add  another  illustration,  which  involves  a 
little  more  algebra,  but  not,  I  think,  more  than  you  can 
understand ;  or,  if  it  does,  you  will  please  pass  over  it 
to  the  next  paragraph.  According  to  a  rule  of  arith- 
metical progression,  the  sum  of  all  the  terms  is  equal 
to  half  the  sum  of  the  extremes  multiplied  into  the 
number  of  terms.  Calling  the  sum  of  the  terms  s,  the 
first  term  a,  the  last  h,  and  the  number  of  terms  n,  and 
we  have  \n(a-\-h)=s ;  or  n(a-\-h)=2s ;  or  a+A=^ ; 
or  a==^ — h ;  or  h—2^- — a.  These  are  only  a  few  of 
the  changes  which  may  be  made  in  the  original  ex- 
pression, still  preserving  the  equality  between  the  quan- 
tities on  the  left  hand  and  those  on  the  right ;  yet  each 
of  these  transformations  expresses  a  new  truth,  indi- 
cating distinct  and  (as  might  be  the  case)  before  un- 
known relations  between  the  several  quantities  of  which 
the  whole  expression  is  composed.  The  last,  for  exam- 
ple, shows  us  that  the  last  term  in  an  arithmetical  se- 
ries is  always  equal  to  twice  the  sum  of  the  whole  se- 
ries divided  by  the  number  of  terms  and  diminished  by 
the  first  term.  In  analytical  formularies,  as  expressions 
of  this  kind  are  called,  the  value  of  a  single  unknown 
quantity  is  sometimes  given  in  a  very  complicated  ex- 
pression, consisting  of  known  quantities ;  but  before 
we  can  ascertain  their  united  value,  we  must  reduce 
them,  by  actually  performing  all  the  additions,  subtrac- 
tions, multiplications,  divisions,  raising  to  powers,  and 


LETTERS  ON  ASTRONOMY. 

extracting  roots,  which  are  denoted  by  the  symbols. 
This  makes  the  actual  calculations  derived  from  such 
formularies  immensely  laborious.  We  have  already 
had  an  instance  of  this  in  the  calculations  made  by 
Lalande  and  Madame  Lepaute,  from  formularies  fur- 
nished by  Clairaut. 

The  analytical  formularies,  contained  in  such  works 
as  La  Place's  '  Mecanique  Celeste,'  exhibit  to  the  eye  of 
the  mathematician  a  record  of  all  the  evolutions  of  the 
bodies  of  the  solar  system  in  ages  past,  and  of  all  the 
changes  they  must  undergo  in  ages  to  come.  Such 
has  been  the  result  of  the  combination  of  transcendent 
mathematical  genius  and  unexampled  labor  and  perse- 
verance, for  the  last  century.  The  learned  societies 
established  in  various  centres  of  civilization  have  more 
especially  directed  their  attention  to  the  advancement 
of  physical  astronomy,  and  have  stimulated  the  spirit 
of  inquiry  by  a  succession  of  prizes,  offered  for  the 
solutions  of  problems  arising  out  of  the  difficulties 
which  were  progressively  developed  by  the  advance- 
ment of  astronomical  knowledge.  Among  these  ques- 
tions, the  determination  of  the  return  of  comets,  and 
the  disturbances  which  they  experience  in  their  course, 
by  the  action  of  the  planets  near  which  they  happen  to 
pass,  hold  a  prominent  place.  In  1826,  the  French 
Institute  offered  a  prize  for  the  determination  of  the 
exact  time  of  the  return  of  Halley's  comet  to  its  peri- 
helion in  1835.  M.  Pontecoulant  aspired  to  the  honor. 
"  After  calculations,"  says  he,  "  of  which  those  alone 
who  have  engaged  in  such  researches  can  estimate  the 
extent  and  appreciate  the  fastidious  monotony,  I  arriv- 
ed at  a  result  which  satisfied  all  the  conditions  propos- 
ed by  the  Institute.  I  determined  the  perturbations 
of  Halley's  comet,  by  taking  into  account  the  simulta- 
neous actions  of  Jupiter,  Saturn,  Uranus,  and  the  Earth ; 
and  I  then  fixed  its  return  to  its  perihelion  for  the  sev- 
enth of  November."  Subsequently  to  this,  however, 
M.  Pontecoulant  made  some  further  researches,  which 
led  him  to  correct  the  former  result ;  and  he  afterwards 


COMETS.  337 

altered  the  time  to  November  fourteenth.  It  actually 
came  to  its  perihelion  on  the  sixteenth,  within  two  days 
of  the  time  assigned. 

Nothing  can  convince  us  more  fully  of  the  complete 
mastery  which  astronomers  have  at  last  acquired  over 
these  erratic  bodies,  than  to  read  in  the  Edinburgh  Re- 
view for  April,  1835,  the  paragraph  containing  the  final 
results  of  all  the  labors  and  anticipations  of  astrono- 
mers, matured  as  they  were,  in  readiness  for  the  ap- 
proaching visitant,  and  then  to  compare  the  prediction 
with  the  event,  as  we  saw  it  fulfilled  a  few  months  af- 
terwards. The  paragraph  was  as  follows:  "On  the 
whole,  it  may  be  considered  as  tolerably  certain,  that 
the  comet  will  become  visible  in  every  part  of  Europe 
about  the  latter  end  of  August,  or  beginning  of  Sep- 
tember, next.  It  will  most  probably  be  distinguishable 
by  the  naked  eye,  like  a  star  of  the  first  magnitude, 
but  with  a  duller  light  than  that  of  a  planet,  and 
surrounded  with  a  pale  nebulosity,  which  will  slightly 
impair  its  splendor.  On  the  night  of  the  seventh  of 
October,  the  comet  will  approach  the  well-known  con- 
stellation of  the  Great  Bear ;  and  between  that  and  the 
eleventh,  it  will  pass  directly  through  the  seven  con- 
spicuous stars  of  that  constellation,  (the  Dipper.)  Tow- 
ards the  end  of  November,  the  comet  will  plunge 
among  the  rays  of  the  sun,  and  disappear,  and  will  not 
issue  from  them,  on  the  other  side,  until  the  end  of  De- 
cember." 

Let  us  now  see  how  far  the  actual  appearances  cor- 
responded to  these  predictions.  The  comet  was  first 
discovered  from  the  observatory  at  Rome,  on  the  morn- 
ing of  the  fifth  of  August ;  by  Professor  Struve,  at  Dor- 
pat,  on  the  twentieth ;  in  England  and  France,  on  the 
twenty-third  ;  and  at  Yale  College,  by  Professor  Loomis 
and  myself,  on  the  thirty-first.  On  the  morning  of  that 
day,  between  two  and  three  o'clock,  in  obedience  to 
the  directions  which  the  great  minds  that  had  marked 
out  its  path  among  the  stars  had  prescribed,  we  direct- 
ed Clarke's  telescope  (a  noble  instrument,  belonging 

29  L.  A. 


338  LETTERS  ON  ASTRONOMY. 

to  Yale  College)  towards  the  northeastern  quarter  of 
the  heavens,  and  lo !  there  was  the  wanderer  so  long 
foretold, — a  dim  speck  of  fog  on  the  confines  of  crea- 
tion. It  carne  on  slowly,  from  night  to  night,  increas- 
ing constantly  in  magnitude  and  brightness,  but  did  not 
become  distinctly  visible  to  the  naked  eye  until  the 
twenty-second  of  September.  For  a  month,  therefore, 
astronomers  enjoyed  this  interesting  spectacle  before  it 
exhibited  itself  to  the  world  at  large.  From  this  time 
it  moved  rapidly  along  the  northern  sky,  until,  about 
the  tenth  of  October,  it  traversed  the  constellation 
of  the  Great  Bear,  passing  a  little  above,  instead  of 
"  through"  the  seven  conspicuous  stars  constituting  the 
Dipper.  At  this  time  it  had  a  lengthened  train,  and 
became,  as  you  doubtless  remember,  an  object  of  uni- 
versal interest.  Early  in  November,  the  comet  ran 
down  to  the  sun,  and  was  lost  in  his  beams  ;  but  on 
the  morning  of  December  thirty-first,  I  again  obtained, 
through  Clarke's  telescope,  a  distinct  view  of  it  on  the 
other  side  of  the  sun,  a  moment  before  the  morning 
dawn. 

This  return  of  Halley's  comet  was  an  astronomical 
event  of  transcendent  importance.  It  was  the  chroni- 
cler of  ages,  and  carried  us,  by  a  few  steps,  up  to  the 
origin  of  time.  If  a  gallant  ship,  which  has  sailed 
round  the  globe,  and  commanded  successively  the  ad- 
miration of  many  great  cities,  diverse  in  language  and 
customs,  is  invested  with  a  peculiar  interest,  what  in- 
terest must  attach  to  one  that  has  made  the  circuit 
of  the  solar  system,  and  fixed  the  gaze  of  successive 
worlds !  So  intimate,  moreover,  is  the  bond  which 
binds  together  all  truths  in  one  indissoluble  chain,  that 
the  establishment  of  one  great  truth  often  confirms  a 
multitude  of  others,  equally  important.  Thus  the  re- 
turn of  Halley's  comet,  in  exact  conformity  with  the 
predictions  of  astronomers,  established  the  truth  of  all 
those  principles  by  which  those  predictions  were  made. 
It  afforded  most  triumphant  proof  of  the  doctrine  of 
universal  gravitation,  and  of  course  of  the  received 


COMETS.  339 

laws  of  physical  astronomy  ;  it  inspired  new  confidence 
in  the  power  and  accuracy  of  that  instrument  (the  cal- 
culus) by  means  of  which  its  elements  had  been  inves- 
tigated ;  and  it  proved  that  the  different  planets,  which 
exerted  upon  it  severally  a  disturbing  force  proportion- 
ed to  their  quantity  of  matter,  had  been  correctly  weigh- 
ed, as  in  a  balance. 

I  must  now  leave  this  wonderful  body  to  pursue  its 
sublime  march  far  beyond  the  confine?  of  Uranus,  (a 
distance  it  has  long  since  reached,)  and  take  a  hasty 
notice  of  two  other  comets,  whose  periodic  returns  have 
also  been  ascertained ;  namely,  those  of  Biela  and 
Encke. 

Biela's  comet  has  a  period  of  six  years  and  three 
quarters.  It  has  its  perihelion  near  the  orbit  of  the 
earth,  and  its  aphelion  a  little  beyond  that  of  Jupiter. 
Its  orbit,  therefore,  is  far  less  eccentric  than  that  of 
Halley's  comet ;  (see  Frontispiece ;)  it  neither  ap- 
proaches so  near  the  sun,  nor  departs  so  far  from  it,  as 
most  other  known  comets :  some,  indeed,  never  come 
nearer  to  the  sun  than  the  orbit  of  Jupiter,  while  they 
recede  to  an  incomprehensible  distance  beyond  the  re- 
motest planet.  We  might  even  imagine  that  they 
would  get  beyond  the  limits  of  the  sun's  attraction ; 
nor  is  this  impossible,  although,  according  to  La  Place, 
the  solar  attraction  is  sensible  throughout  a  sphere 
whose  radius  is  a  hundred  millions  of  times  greater 
than  the  distance  of  the  earth  from  the  sun,  or  nearly 
ten  thousand  billions  of  miles. 

Some  months  before  the  expected  return  of  Biela's 
comet,  in  1832,  it  was  announced  by  astronomers,  who 
had  calculated  its  path,  that  it  would  cross  the  plane 
of  the  earth's  orbit  very  near  to  the  earth5s  path,  so 
that,  should  the  earth  happen  at  the  time  to  be  at  that 
point  of  her  revolution,  a  collision  might  take  place. 
This  announcement  excited  so  much  alarm  among  the 
ignorant  classes  in  France,  that  it  was  deemed  expedi- 
ent by  the  French  academy,  that  one  of  their  number 
should  prepare  and  publish  an  article  on  the  subject, 


340  LETTERS  ON  ASTRONOMY. 

with  the  express  view  of  allaying  popular  apprehension. 
This  task  was  executed  by  M.  Arago.  He  admitted 
that  the  earth  would  in  fact  pass  so  near  the  point 
where  the  comet  crossed  the  plane  of  its  orbit,  that, 
should  they  chance  to  meet  there,  the  earth  would  be 
enveloped  in  the  nebulous  atmosphere  of  the  comet. 
He,  however,  showed  that  the  earth  would  not  be  near 
that  point  at  the  same  time  with  the  comet,  but  fifty 
millions  of  miles  from  it. 

The  comet  came  at  the  appointed  time,  but  was  so 
exceedingly  faint  and  small,  that  it  was  visible  only  to 
the  largest  telescopes.  In  one  respect,  its  diminutive 
size  and  feeble  light  enhanced  the  interest  with  which 
it  was  contemplated  ;  for  it  was  a  sublime  spectacle  to 
see  a  body,  which,  as  projected  on  the  celestial  vault, 
even  when  magnified  a  thousand  times,  seemed  but 
a  dim  speck  of  fog,  still  pursuing  its  way,  in  obedi- 
ence to  the  laws  of  universal  gravitation,  with  the 
same  regularity  as  Jupiter  and  Saturn.  We  are  apt 
to  imagine  that  a  body,  consisting  of  such  light  mate- 
rials that  it  can  be  compared  only  to  the  thinnest  fog, 
would  be  dissipated  and  lost  in  the  boundless  regions 
of  space  ;  but  so  far  is  this  from  the  truth,  that,  when 
subjected  to  the  action  of  the  same  forces  of  projection 
and  solar  attraction,  it  will  move  through  the  void  re- 
gions of  space,  and  will  describe  its  own  orbit  about 
the  sun  with  the  same  unerring  certainty,  as  the  dens- 
est bodies  of  the  system. 

Encke's  comet,  by  its  frequent  returns,  (once  in 
three  and  a  third  years,)  affords  peculiar  facilities  for 
ascertaining  the  laws  of  its  revolution  ;  and  it  has  kept 
the  appointments  made  for  it  with  great  exactness.  On 
its  return  in  1839,  it  exhibited  to  the  telescope  a  glob- 
ular mass  of  nebulous  matter,  resembling  fog,  and 
moved  towards  its  perihelion  with  great  rapidity.  It 
makes  its  entire  excursions  within  the  orbit  of  Jupiter. 

But  what  has  made  Encke's  comet  particularly  fa- 
mous, is  its  having  first  revealed  to  us  the  existence  of 
a  resisting  medium  in  the  planetary  spaces.  It  has 


COMETS.  341 

long  been  a  question,  whether  the  earth  and  planets 
revolve  in  a  perfect  void,  or  whether  a  fluid  of  extreme 
rarity  may  not  be  diffused  through  space.  A  perfect 
vacuum  was  deemed  most  probable,  because  no  such 
effects  on  the  motions  of  the  planets  could  be  detected 
as  indicated  that  they  encountered  a  resisting  medium. 
But  a  feather,  or  a  lock  of  cotton,  propelled  with  great 
velocity,  might  render  obvious  the  resistance  of  a  me- 
dium which  would  not  be  perceptible  in  the  motions 
of  a  cannon  ball.  Accordingly,  Encke's  comet  is 
thought  to  have  plainly  suffered  a  retardation  from  en- 
countering a  resisting  medium  in  the  planetary  regions. 
The  effect  of  this  resistance,  from  the  first  discovery  of 
the  comet  to  the  present  time,  has  been  to  diminish  the 
time  of  its  revolution  about  two  days.  Such  a  resist- 
ance, by  destroying  a  part  of  the  projectile  force,  would 
cause  the  comet  to  approach  nearer  to  the  sun,  and 
thus  to  have  its  periodic  time  shortened.  The  ul- 
timate effect  of  this  cause  will  be  to  bring  the  comet 
nearer  to  the  sun,  at  every  revolution,  until  it  finally 
falls  into  that  luminary,  although  many  thousand  years 
will  be  required  to  produce  this  catastrophe.  It  is  con- 
ceivable, indeed,  that  the  effects  of  such  a  resistance 
may  be  counteracted  by  the  attraction  of  one  or  more 
of  the  planets,  near  which  it  may  pass  in  its  successive 
returns  to  the  sun.  Still,  it  is  not  probable  that  this 
cause  will  exactly  counterbalance  the  other  ;  so  that,  if 
there  is  such  an  elastic  medium  diffused  through  the 
planetary  regions,  it  must  follow  that,  in  the  lapse  of 
ages,  every  comet  will  fall  into  the  sun.  Newton  con- 
jectured that  this  would  be  the  case,  although  he  did 
not  found  his  opinion  upon  the  existence  of  such  a  re- 
sisting medium  as  is  now  detected.  To  such  an  opin- 
ion he  adhered  to  the  end  of  life.  At  the  age  of 
eighty-three,  in  a  conversation  with  his  nephew,  he  ex- 
pressed himself  thus :  "  I  cannot  say  when  the  comet 
of  1680  will  fall  into  the  sun  ;  possibly  after  five  or  six 
revolutions ;  but  whenever  that  time  shall  arrive,  the 
heat  of  the  sun  will  be  raised  by  it  to  such  a  point,  that 
29* 


342 


LETTERS  ON  ASTRONOMY. 


our  globe  will  be  burned,  and  all  the  animals  upon  it 
will  perish." 

Of  the  physical  nature  of  comets  little  is  understood. 
The  greater  part  of  them  are  evidently  mere  masses  of 
vapor,  since  they  permit  very  small  stars  to  be  seen 
through  them.  In  September,  1832,  Sir  John  Her- 
schel,  when  observing  Biela's  comet,  saw  that  body  pass 
directly  between  his  eye  and  a  small  cluster  of  minute 
telescopic  stars  of  the  sixteenth  or  seventeenth  magni- 
tude. This  little  constellation  occupied  a  space  in  the 
heavens,  the  breadth  of  which  was  not  the  twentieth 
part  of  that  of  the  moon ;  yet  the  whole  of  the  cluster 
was  distinctly  visible  through  the  comet.  "A  more 
striking  proof,"  says  Sir  John  Herschel,  "  could  not 
have  been  afforded,  of  the  extreme  transparency  of  the 
matter  of  which  this  comet  consists.  The  most  trifling 
fog  would  have  entirely  effaced  this  group  of  stars,  yet. 
they  continued  visible  through  a  thickness  of  the  comet 
which,  calculating  on  its  distance  and  apparent  diame- 
ter, must  have  exceeded  fifty  thousand  miles,  at  least 
towards  its  central  parts."  From  this  and  similar  ob- 
servations, it  is  inferred,  that  the  nebulous  matter  of 
comets  is  vastly  more  rare  than  that  of  the  air  we 
breathe,  and  hence,  that,  were  more  or  less  of  it  to  be 
mingled  with  the  earth's  atmosphere,  it  would  not  be 
perceived,  although  it  might  possibly  render  the  air  tin- 
wholesome  for  respiration.  M.  Arago,  however,  is  of 
the  opinion,  that  some  comets,  at  least,  have  a  solid 
nucleus.  It  is  difficult,  on  any  other  supposition,  to 
account  for  the  strong  light  which  some  of  them  have 
exhibited, — a  light  sufficiently  intense  to  render  them 
visible  in  the  day-time,  during  the  presence  of  the  sun. 
The  intense  heat  to  which  comets  are  subject,  in  ap- 
proaching so  near  the  sun  as  some  of  them  do,  is  alleged 
as  a  sufficient  reason  for  the  great  expansion  of  the 
thin  vapory  atmospheres  which  form  their  tails  ;  and  the 
inconceivable  cold  to  which  they  are  subject,  in  receding 
to  such  a  distance  from  the  sun,  is  supposed  to  account 
for  the  condensation  of  the  same  matter  until  it  returns 


COMETS.  343 

to  its  original  dimensions.  Thus  the  great  comet  of 
1680,  at  its  perihelion,  approached  within  one  hun- 
dred and  forty-six  thousand  miles  of  the  surface  of 
the  sun,  a  distance  of  only  one  sixth  part  of  the  sun's 
diameter.  The  heat  which  it  must  have  received  was 
estimated  to  be  equal  to  twenty-eight  thousand  times 
that  which  the  earth  receives  in  the  same  time,  and 
two  thousand  times  hotter  than  red-hot  iron.  This 
temperature  would  be  sufficient  to  volatilize  the  most 
obdurate  substances,  and  to  expand  the  vapor  to  vast 
dimensions ;  and  the  opposite  effects  of  the  extreme 
cold  to  which  it  would  be  subject  in  the  regions  remote 
from  the  sun  would  be  adequate  to  condense  it  into  its 
former  volume.  This  explanation,  however,  does  not 
account  for  the  direction  of  the  tail,  extending,  as  it 
usually  does,  only  in  a  line  opposite  to  the  sun.  Some 
writers,  therefore,  suppose  that  the  nebulous  matter  of 
the  comet,  after  being  expanded  to  such  a  volume  that 
the  particles  are  no  longer  attracted  to  the  nucleus,  un- 
less by  the  slightest  conceivable  force,  are  carried  off 
in  a  direction  from  the  sun,  by  the  impulse  of  the 
solar  rays  themselves.  But  to  assign  such  a  power  to 
the  sun's  rays,  while  they  have  never  been  proved  to 
have  any  momentum,  is  unphilosophical ;  and  we  are 
compelled  to  place  the  phenomena  of  comets'  tails 
among  the  points  of  astronomy  yet  to  be  explained. 

Since  comets  which  approach  very  near  the  sun,  like 
the  comet  of  1680,  cross  the  orbits  of  all  the  planets, 
the  possibility  that  one  of  them  may  strike  the  earth  has 
frequently  been  suggested.  Still  it  may  quiet  our  ap- 
prehensions on  this  subject,  to  reflect  on  the  vast  am- 
plitude of  the  planetary  spaces,  in  which  these  bodies 
are  not  crowded  together,  as  we  see  them  erroneously 
represented  in  orreries  and  diagrams,  but  are  sparsely 
scattered  at  immense  distances  from  each  other.  They 
are  like  insects  flying,  singly,  in  the  expanse  of  heaven. 
If  a  comet's  tail  lay  with  its  axis  in  the  plane  of  the 
ecliptic  when  it  was  near  the  sun,  we  can  imagine 
that  the  tail  might  sweep  over  the  earth ;  but  the 


344  LETTERS  ON  ASTRONOMY. 

tail  may  be  situated  at  any  angle  with  the  ecliptic, 
as  well  as  in  the  same  plane  with  it,  and  the  chances 
that  it  will  not  be  in  the  same  plane  are  almost  infinite. 
It  is  also  extremely  improbable  that  a  comet  will  cross 
the  plane  of  the  ecliptic  precisely  at  the  earth's  path  in 
that  plane,  since  it  may  as  probably  cross  it  at  any  oth- 
er point  nearer  or  more  remote  from  the  sun.  A  French 
writer  of  some  eminence  (Du  Sejour)  has  discussed 
this  subject  with  ability,  and  arrived  at  the  following 
conclusions :  That  of  all  the  comets  whose  paths  had 
been  ascertained,  none  could  pass  nearer  to  the  earth 
than  about  twice  the  moon's  distance  ;  and  that  none 
ever  did  pass  nearer  to  the  earth  than  nine  times  the 
moon's  distance.  The  comet  of  1770,  already  men- 
tioned, which  became  entangled  among  the  satellites 
of  Jupiter,  came  within  this  limit.  Some  have  taken 
alarm  at  the  idea  that  a  comet,  by  approaching  very 
near  to  the  earth,  might  raise  so  high  a  tide,  as  to  en- 
danger the  safety  of  maritime  countries  especially  :  but 
this  writer  shows,  that  the  comet  could  not  possibly  re- 
main more  than  two  hours  so  near  the  earth  as  a  fourth 
part  of  the  moon's  distance ;  and  it  could  not  remain 
even  so  long,  unless  it  passed  the  earth  under  very  pe- 
culiar circumstances.  For  example,  if  its  orbit  were 
nearly  perpendicular  to  that  of  the  earth,  it  could  not 
remain  more  than  half  an  hour  in  such  a  position.  Un- 
der such  circumstances,  the  production  of  a  tide  would 
be  impossible.  Eleven  hours,  at  least,  would  be  neces- 
sary to  enable  a  comet  to  produce  an  effect  on  the  wa- 
ters of  the  earth,  from  which  the  injurious  effects  so 
much  dreaded  would  follow.  The  final  conclusion  at 
which  he  arrives  is,  that  although,  in  strict  geometrical 
rigor,  it  is  not  physically  impossible  that  a  comet  should 
encounter  the  earth,  yet  the  probability  of  such  an  event 
is  absolutely  nothing. 

M.  Arago,  also,  has  investigated  the  probability  of 
such  a  collision  on  the  mathematical  doctrine  of  chan- 
ces, and  remarks  as  follows  :  "  Suppose,  now,  a  comet, 
of  which  we  know  nothing  but  that,  at  its  perihelion,  it 


COMETS.  345 

will  be  nearer  the  sun  than  we  are,  and  that  its  diame- 
ter is  equal  to  one  fourth  that  of  the  earth  ;  the  doctrine 
of  chances  shows  that,  out  of  two  hundred  and  eighty- 
one  millions  of  cases,  there  is  but  one  against  us ;  but 
one,  in  which  the  two  bodies  could  meet." 

La  Place  has  assigned  the  consequences  that  would 
result  from  a  direct  collision  between  the  earth  and  a 
comet.  "  It  is  easy,"  says  he,  "  to  represent  the  effects 
of  the  shock  produced  by  the  earth's  encountering  a 
comet.  The  axis  and  the  motion  of  rotation  changed ; 
the  waters  abandoning  their  former  position  to  precipi- 
tate themselves  towards  the  new  equator ;  a  great  part 
of  men  and  animals  whelmed  in  a  universal  deluge,  or 
destroyed  by  the  violent  shock  imparted  to  the  terres- 
trial globe ;  entire  species  annihilated ;  all  the  monu- 
ments of  human  industry  overthrown ; — such  are  the 
disasters  which  the  shock  of  a  comet  would  necessarily 
produce."  La  Place,  nevertheless,  expresses  a  decid- 
ed opinion  that  the  orbits  of  the  planets  have  never  yet 
been  disturbed  by  the  influence  of  comets.  Comets, 
moreover,  have  been,  and  are  still  to  some  degree, 
supposed  to  exercise  much  influence  in  the  affairs  of 
this  world,  affecting  the  weather,  the  crops,  the  public 
health,  and  a  great  variety  of  atmospheric  commotions. 
Even  Halley,  finding  that  his  comet  must  have  been 
near  the  earth  at  the  time  of  the  Deluge,  suggested  the 
possibility  that  the  comet  caused  that  event, — an  idea 
which  was  taken  up  by  Whiston,  and  formed  into  a 
regular  theory.  In  Gregory's  Astronomy,  an  able  work, 
published  at  Oxford  in  1702,  the  author  remarks,  that 
among  all  nations  and  in  all  ages,  it  has  been  observed, 
that  the  appearance  of  a  comet  has  always  been  fol- 
lowed by  great  calamities ;  and  he  adds,  "  it  does  not 
become  philosophers  lightly  to  set  down  these  things  as 
fables."  Among  the  various  things  ascribed  to  comets 
by  a  late  English  writer,  are  hot  and  cold  seasons,  tem- 
pests, hurricanes,  violent  hail-storms,  great  falls  of  snow, 
heavy  rains,  inundations,  droughts,  famines,  thick  fogs, 
flies,  grasshoppers,  plague,  dysentery,  contagious  dis- 


346  LETTERS  ON  ASTRONOMY. 

eases  among  animals,  sickness  among  cats,  volcanic 
eruptions,  and  meteors,  or  shooting  stars.  These  no- 
tions are  too  ridiculous  to  require  a  distinct  refutation ; 
and  I  will  only  add,  that  we  have  no  evidence  that 
comets  have  hitherto  ever  exercised  the  least  influence 
upon  the  affairs  of  this  world ;  and  we  still  remain  in 
darkness,  with  respect  to  their  physical  nature,  and  the 
purposes  for  which  they  were  created. 


LETTER  XXVII. 

METEORIC   SHOWERS. 

"Oft  shall  them  see,  ere  brooding  storms  arise, 
Star  after  star  glide  headlong  down  the  skies, 
And,  where  they  shot,  long  trails  of  lingering  light 
Sweep  far  behind,  and  gild  the  shades  of  night." — Virgil. 

FEW  subjects  of  astronomy  have  excited  a  more 
general  interest,  for  several  years  past,  than  those  ex- 
traordinary exhibitions  of  shooting  stars,  which  have  ac- 
quired the  name  of  meteoric  showers.  My  reason  for 
introducing  the  subject  to  your  notice,  in  this  place,  is, 
that  these  small  bodies  are,  as  I  believe,  derived  from 
nebulous  or  cometaf-y  bodies,  which  belong  to  the  solar 
system,  and  which,  therefore,  ought  to  be  considered, 
before  we  take  our  leave  of  this  department  of  creation, 
and  naturally  come  next  in  order  to  comets. 

The  attention  of  astronomers  was  particularly  direct- 
ed to  this  subject  by  the  extraordinary  shower  of  me- 
teors which  occurred  on  the  morning  of  the  thirteenth 
of  November,  1833.  I  had  the  good  fortune  to  wit- 
ness these  grand  celestial  fire-works,  and  felt,  a  strong 
desire  that  a  phenomenon,  which,  as  it  afterwards  ap- 
peared, was  confined  chiefly  to  North  America,  should 
here  command  that  diligent  inquiry  into  its  causes, 
which  so  sublime  a  spectacle  might  justly  claim. 

As  I  think  you  were  not  so  happy  as  to  witness  this 
magnificent  display,  I  will  endeavor  to  give  you  some 
faint  idea  of  it,  as  it  appeared  to  me  a  little  before  day- 


METEORIC  SHOWERS.  347 

break.  Imagine  a  constant  succession  of  fire-balls,  re- 
sembling sky-rockets,  radiating  in  all  directions  from  a 
point  in  the  heavens  a  few  degrees  southeast  of  the  ze- 
nith, and  following  the  arch  of  the  sky  towards  the  ho- 
rizon. They  commenced  their  progress  at  different 
distances  from  the  radiating  point ;  but  their  directions 
were  uniformly  such,  that  the  lines  they  described,  if 
produced  upwards,  would  all  have  met  in  the  same  part 
of  the  heavens.  Around  this  point,  or  imaginary  ra- 
diant, was  a  circular  space  of  several  degrees,  within 
which  no  meteors  were  observed.  The  balls,  as  they 
travelled  down  the  vault,  usually  left  after  them  a  vivid 
streak  of  light ;  and,  just  before  they  disappeared,  ex- 
ploded, or  suddenly  resolved  themselves  into  smoke. 
No  report  of  any  kind  was  observed,  although  we  lis- 
tened attentively. 

Beside  the  foregoing  distinct  concretions,  or  individ- 
ual bodies,  the  atmosphere  exhibited  phosphoric  lines, 
following  in  the  train  of  minute  points,  that  shot  off  in 
the  greatest  abundance  in  a  northwesterly  direction. 
These  did  not  so  fully  copy  the  figure  of  the  sky,  but 
moved  in  paths  more  nearly  rectilinear,  and  appeared 
to  be  much  nearer  the  spectator  than  the  fire-balls. 
The  light  of  their  trains  was  also  of  a  paler  hue,  not 
unlike  that  produced  by  writing  with  a  stick  of  phos- 
phorus on  the  walls  of  a  dark  room.  The  number  of 
these  luminous  trains  increased  and  diminished  alter- 
nately, now  and  then  crossing  the  field  of  view,  like 
snow  drifted  before  the  wind,  although,  in  fact,  their 
course  was  towards  the  wind. 

From  these  two  varieties,  we  were  presented  with 
meteors  of  various  sizes  and  degrees  of  splendor :  some 
were  mere  points,  while  others  were  larger  and  bright- 
er than  Jupiter  or  Venus ;  and  one,  seen  by  a  credible 
witness,  at  an  earlier  hour,  was  judged  to  be  nearly  as 
large  as  the  moon.  The  flashes  of  light,  although  less 
intense  than  lightning,  were  so  bright,  as  to  awaken 
people  in  their  beds.  One  ball  that  shot  off  in  the 
northwest  direction,  and  exploded  a  little  northward  of 


348  LETTERS  ON  ASTRONOMY. 

the  star  Capella,  left,  just  behind  the  place  of  explosion, 
a  phosphorescent  train  of  peculiar  beauty.  This  train 
was  at  first  nearly  straight,  but  it  shortly  began  to  con- 
tract in  length,  to  dilate  in  breadth,  and  to  assume  the 
figure  of  a  serpent  drawing  itself  up,  until  it  appeared 
like  a  small  luminous  cloud  of  vapor.  This  cloud  was 
borne  eastward,  (by  the  wind,  as  was  supposed,  which 
was  blowing  gently  in  that  direction,)  opposite  to  the 
direction  in  which  the  meteor  itself  had  moved,  remain- 
ing in  sight  several  minutes.  The  point  from  which 
the  meteors  seemed  to  radiate  kept  a  fixed  position 
among  the  stars,  being  constantly  near  a  star  in  Leo, 
called  Gamma  Leonis. 

Such  is  a  brief  description  of  this  grand  and  beauti- 
ful display,  as  I  saw  it  at  New  Haven.  The  newspa- 
pers shortly  brought^us  intelligence  of  similar  appear- 
ances in  all  parts  of  the  United  States,  and  many  mi- 
nute descriptions  were  published  by  various  observers ; 
from  which  it  appeared,  that  the  exhibition  had  been 
marked  by  very  nearly  the  same  characteristics  wher- 
ever it  had  been  seen.  Probably  no  celestial  phenom- 
enon has  ever  occurred  in  this  country,  since  its  first 
settlement,  which  was  viewed  with  so  much  admiration 
and  delight  by  one  class  of  spectators,  or  with  so  much 
astonishment  and  fear  by  another  class.  It  striking- 
ly evinced  the  progress  of  knowledge  and  civilization, 
that  the  latter  class  was  comparatively  so  small,  although 
it  afforded  some  few  examples  of  the  dismay  with  which, 
in  barbarous  ages  of  the  world,  such  spectacles  as  this 
were  wont  to  be  regarded.  One  or  two  instances  were 
reported,  of  persons  who  died  with  terror ;  many  oth- 
ers thought  the  last  great  day  had  come ;  and  the  un- 
tutored black  population  of  the  South  gave  expression 
to  their  fears  in  cries  and  shrieks. 

After  collecting  and  collating  the  accounts  given  in 
all  the  periodicals  of  the  country,  and  also  in  numerous 
letters  addressed  either  to  my  scientific  friends  or  to  my- 
self, the  following  appeared  to  be  the  leading  facts  at- 
tending the  phenomenon.  The  shower  pervaded  near- 


METEORIC   SHOWERS.  349 

ly  the  whole  of  North  America,  having  appeared  in 
nearly  equal  splendor  from  the  British  possessions  on 
the  north  to  the  West-India  Islands  and  Mexico  on 
the  south,  and  from  sixty-one  degrees  of  longitude  east 
of  the  American  coast,  quite  to  the  Pacific  Ocean  on 
the  west.  Throughout  this  immense  region,  the  dura- 
tion was  nearly  the  same.  The  meteors  began  to  at- 
tract attention  by  their  unusual  frequency  and  brillian- 
cy, from  nine  to  twelve  o'clock  in  the  evening ;  were 
most  striking  in  their  appearance  from  two  to  five ;  ar- 
rived at  their  maximum,  in  many  places,  about  four 
o'clock ;  and  continued  until  rendered  invisible  by  the 
light  of  day.  The  meteors  moved  either  in  right  lines, 
or  in  such  apparent  curves,  as,  upon  optical  principles, 
can  be  resolved  into  right  lines.  Their  general  tenden- 
cy was  towards  the  northwest,  although,  by  the  effect 
of  perspective,  they  appeared  to  move  in  various  direc- 
tions. 

Such  were  the  leading  phenomena  of  the  great  me- 
teoric shower  of  November  13,  1833.  For  a  fuller  de- 
tail of  the  facts,  as  well  as  of  the  reasonings  that  were 
built  on  them,  I  must  beg  leave  to  refer  you  to  some 
papers  of  mine  in  the  twenty-fifth  and  twenty-sixth 
volumes  of  the  American  Journal  of  Science. 

Soon  after  this  remarkable  occurrence,  it  was  ascer- 
tained that  a  similar  meteoric  shower  had  appeared  in 
1799,  and,  what  was  remarkable,  almost  at  exactly 
the  same  time  of  year,  namely,  on  the  morning  of  the 
twelfth  of  November ;  and  we  were  again  surprised  as 
well  as  delighted,  at  receiving  successive  accounts  from 
different  parts  of  the  world  of  the  phenomenon,  as  hav- 
ing occurred  on  the  morning  of  the  same  thirteenth  of 
November,  in  1830,  1831,  and  1832.  Hence  this  was 
evidently  an  event  independent  of  the  casual  changes 
of  the  atmosphere ;  for,  having  a  periodical  return,  it 
was  undoubtedly  to  be  referred  to  astronomical  causes, 
and  its  recurrence,  at  a  certain  definite  period  of  the 
year,  plainly  indicated  some  relation  to  the  revolution 
of  the  earth  around  the  sun.-  It  remained,  however,  to 
30  L.  A. 


350  LETTERS  ON  ASTRONO3fiT* 

develope  the  nature  of  this  relation,  by  investigating', 
if  possible,  the  origin  of  the  meteors.  The  views  to 
which  I  was  led  on  this  subject  suggested  the  probabil- 
ity that  the  same  phenomenon  would  recur  on  the  cor- 
responding seasons  of  the  year,  for  at  least  several  years 
afterwards ;  and  such  proved  to  be  the  fact,  although 
the  appearances,  at  every  succeeding  return,  were  less 
and  less  striking,  until  1839,  when,  so  far  as  I  have 
heard,  they  ceased  altogether. 

Mean-while,  two  other  distinct  periods  of  meteoric 
showers  have,  as  already  intimated,  been  determined  ; 
namely,  about  the  ninth  of  August,  and  seventh  of  De- 
cember. The  facts  relative  to  the  history  of  these 
periods  have  been  collected  with  great  industry  by  Mr. 
Edward  C.  Herrick  ;  and  several  of  the  most  ingenious 
and  most  useful  conclusions,  respecting  the  laws  that 
regulate  these  singular  exhibitions,  have  been  deduced 
by  Professor  Twining.  Several  of  the  most  distin- 
guished astronomers  of  the  Old  World,  also,  have  en- 
gaged in  these  investigations  with  great  zeal,  as  Messrs. 
Arago  and  Biot,  of  Paris  ;  Doctor  Olbers,  of  Bremen  ; 
M.  Wartmann,  of  Geneva  ;  and  M.  Quetelet,  of  Brussels. 

But  you  will  be  desirous  to  learn  what  are  the  con- 
clusions which  have  been  drawn  respecting  these  new 
and  extraordinary  phenomena  of  the  heavens.  As 
the  inferences  to  which  I  was  led,  as  explained  in 
the  twenty-sixth  volume  of  the  '  American  Journal  of 
Science,'  have,  at  least  in  their  most  important  points, 
been  sanctioned  by  astronomers  of  the  highest  respec- 
tability, I  will  venture  to  give  you  a  brief  abstract  of 
them,  with  such  modifications  as  the  progress  of  inves- 
tigation since  that  period  has  rendered  necessary. 

The  principal  questions  involved  in  the  inquiry  were 
the  following : — Was  the  origin  of  the  meteors  within 
the  atmosphere,  or  beyond  it  ?  What  was  the  height 
of  the  place  above  the  surface  of  the  earth  ?  By  what 
force  were  the  meteors  drawn  or  impelled  towards  the 
earth  ?  In  what  directions  did  they  move  ?  With 
what  velocity  ?  What  was  the  cause  of  their  light  and 


METEORIC   SHOWERS.  351 

heat  ?  Of  what  size  were  the  larger  varieties  ?  At  what 
height  above  the  earth  did  they  disappear  ?  What  was 
the  nature  of  the  luminous  trains  which  sometimes  re- 
mained behind  ?  What  sort  of  bodies  were  the  me- 
teors themselves  ;  of  what  kind  of  matter  constituted  ; 
and  in  what  manner  did  they  exist  before  they  fell  to 
the  earth  1  Finally,  what  relations  did  the  source  from 
which  they  emanated  sustain  to  our  earth  ? 

In  the  first  place,  the  meteors  had  their  origin  be- 
yond the  limits  of  our  atmosphere.  We  know  wheth- 
er a  given  appearance  in  the  sky  is  within  the  atmos- 
phere or  beyond  it,  by  this  circumstance:  all  bodies 
near  the  earth,  including  the  atmosphere  itself,  have  a 
common  motion  with  the  earth  around  its  axis  from  west 
to  east.  When  we  see  a  celestial  object  moving  regu- 
larly from  west  to  east,  at  the  same  rate  as  the  earth 
moves,  leaving  the  stars  behind,  we  know  it  is  near  the 
earth,  and  partakes,  in  common  with  the  atmosphere, 
of  its  diurnal  rotation :  but  when  the  earth  leaves  the 
object  behind ;  or,  in  other  words,  when  the  object 
moves  westward  along  with  the  stars,  then  we  know 
that  it  is  so  distant  as  not  to  participate  in  the  diurnal 
revolution  of  the  earth,  and  of  course  to  be  beyond  the 
atmosphere.  The  source  from  which  the  meteors  em- 
anated thus  kept  pace  with  the  stars,  and  hence  was 
beyond  the  atmosphere. 

In  the  second  place,  the  height  of  the  place  whence 
the  meteors  proceeded  was  very  great,  but  it  has  not 
yet  been  accurately  determined.  Regarding  the  body 
whence  the  meteors  emanated  after  the  similitude  of  a 
cloud,  it  seemed  possible  to  obtain  its  height  in  the 
same  manner  as  we  measure  the  height  of  a  cloud,  or 
indeed  the  height  of  the  moon.  Although  we  could 
not  see  the  body  itself,  yet  the  part  of  the  heavens 
whence  the  meteors  came  would  indicate  its  position. 
This  point  we  called  the  radiant;  and  the  question 
was,  whether  the  radiant  was  projected  by  distant  ob- 
servers on  different  parts  of  the  sky ;  that  is,  whether 
it  had  any  parallax.  I  took  much  pains  to  ascertain 
the  truth  of  this  matter,  by  corresponding  with  various 


352  LETTERS  ON  ASTRONOMY. 

observers  in  different  parts  of  the  United  States,  who 
had  accurately  noted  the  position  of  the  radiant  among 
the  fixed  stars,  and  supposed  I  had  obtained  such  ma- 
terials as  would  enable  us  to  determine  the  parallax,  at 
least  approximately  ;  although  such  discordances  exist- 
ed in  the  evidence  as  reasonably  to  create  some  distrust 
of  its  validity.  Putting  together,  however,  the  best  ma- 
terials I  could  obtain,  I  made  the  height  of  the  radiant 
above  the  surface  of  the  earth  twenty-two  hundred  and 
thirty-eight  miles.  When,  however,  I  afterwards  ob- 
tained, as  I  supposed,  some  insight  into  the  celestial 
origin  of  the  meteors,  I  at  once  saw  that  the  meteoric 
body  must  be  much  further  off  than  this  distance  ;  and 
my  present  impression  is,  that  we  have  not  the  means 
of  determining  what  its  height  really  is.  We  may  safe- 
ly place  it  at  many  thousand  miles. 

In  the  third  place,  with  respect  to  the  force  by  which 
the  meteors  were  drawn  or  impelled  towards  the  earth, 
my  first  impression  was,  that  they  fell  merely  by  the 
force  of  gravity  ;  but  the  velocity  which,  on  careful  in- 
vestigation by  Professor  Twining  and  others,  has  been 
ascribed  to  them,  is  greater  than  can  possibly  result 
from  gravity,  since  a  body  can  never  acquire,  by  grav- 
ity alone,  a  velocity  greater  than  about  seven  miles 
per  second.  Some  other  cause,  beside  gravity,  must 
therefore  act,  in  order  to  give  the  meteors  so  great  an 
apparent  velocity. 

In  the  fourth  place,  the  meteors  fell  towards  the 
earth  in  straight  lines,  and  in  directions  which,  with- 
in considerable  distances,  were  nearly  parallel  tvith 
each  other.  The  courses  are  inferred  to  have  been  in 
straight  lines,  because  no  others  could  have  appeared 
to  spectators  in  different  situations  to  have  described 
arcs  of  great  circles.  In  order  to  be  projected  into 
the  arc  of  a  great  circle,  the  line  of  descent  must  be  in 
a  plane  passing  through  the  eye  of  the  spectator ;  and 
the  intersection  of  such  planes,  passing  through  the  eyes 
of  different  spectators,  must  be  straight  lines.  The 
lines  of  direction  are  inferred  to  have  been  parallel,  on 
account  of  their  apparent  radiation  from  one  point,  that 


METEORIC  SHOWERS. 


353 


being  the  vanishing  point  of  parallel  lines.  This  may 
appear  to  you  a  little  paradoxical,  to  infer  that  lines  are 
parallel,  because  they  diverge  from  one  and  the  same 
point ;  but  it  is  a  well-known  principle  of  perspective, 
that  parallel  lines,  when  continued  to  a  great  distance 
from  the  eye,  appear  to  converge  towards  the  remoter 
end.  You  may  observe  this  in  two  long  rows  of  trees, 
or  of  street  lamps. 

Some  idea  of  the  manner  in  which  the  meteors  fell, 
and  of  the  reason  of  their  apparent  radiation  from  a 
common  point,  may  be  gathered  from  the  annexed  di- 
agram. Let  ABC,  Fig.  69,  represent  the  vault  of  the 

Fig.  69. 


30* 


354  LETTERS  ON  ASTRONOMY. 

sky,  the  centre  of  which,  D,  being  the  place  of  the  spec- 
tator. Let  1,  2,  3,  &c.,  represent  parallel  lines  direct- 
ed towards  the  earth,  A  luminous  body  descending 
through  1'  1,  coinciding  with  the  line  D  E,  coincident 
with  the  axis  of  vision,  (or  the  line  drawn  from  the  me- 
teoric body  to  the  eye,)  would  appear  stationary  all 
the  while  at  1',  because  distant  bodies  always  appear 
stationary  when  they  are  moving  either  directly  towards 
us  or  directly  from  us.  A  body  descending  through 
2  2,  would  seem  to  describe  the  short  arc  2'  2',  ap- 
pearing to  move  on  the  concave  of  the  sky  between  the 
lines  drawn  from  the  eye  to  the  two  extremities  of  its 
line  of  motion ;  and,  for  a  similar  reason,  a  body  de- 
scending through  3  3,  would  appear  to  describe  the 
larger  arc  3'  3'.  Hence,  those  meteors  which  fell  near- 
er to  the  axis  of  vision,  would  describe  shorter  arcs,  and 
move  slower,  while  those  which  were  further  from  the 
axis  and  nearer  ;tfo 'horizon  would  appear  to  describe 
longer  arcs,  anc^ta  move  with  greater  velocity  ;  the  me- 
teors would  .allj,seem  to  radiate  from  a  common  centre, 
namely,  the  point  where  the  axis  of  vision  met  the  ce- 
lestial vault;  and  if  any  meteor  chanced  to  move  di- 
rectly in  the  line  of  vision,  it  would  be  seen  as  a  lumi- 
nous body,  stationary,  for  a  few  seconds,  at  the  centre 
of  radiation.  To  see  how  exactly  the  facts,  as  observ- 
ed, corresponded  to  these  inferences,  derived  from  the 
supposition  that  the  meteors  moved  in  parallel  lines, 
take  the  following  description,  as  given  immediately  after 
the  occurrence,  by  Professor  Twining.  "  In  the  vicin- 
ity of  the  radiant  point,  a  few  star-like  bodies  were  ob- 
served, possessing  very  little  motion,  and  leaving  very 
little  length  of  trace.  Further  off,  the  motions  were  more 
rapid  and  the  traces  longer ;  and  most  rapid  of  all,  and 
longest  in  their  traces,  were  those  which  originated  but 
a  few  degrees  above  the  horizon,  and  descended  down 
to  it." 

In  the  fifth  place,  had  the  meteors  come  from  a  point 
twenty-two  hundred  and  thirty-eight  miles  from  the 
earth,  and  derived  their  apparent  velocity  from  gravity 


METEORIC  SHOWERS.  355 

alone,  then  it  would  be  found,  by  a  very  easy  calcula- 
tion, that  their  actual  velocity  was  about  four  miles  per 
second ;  but,  as  already  intimated,  the  velocity  observ- 
ed was  estimated  much  greater  than  could  be  account- 
ed for  on  these  principles ;  not  less,  indeed,  than  four- 
teen miles  per  second,  and,  in  some  instances,  much 
greater  even  than  this.  The  motion  of  the  earth  in  its 
orbit  is  about  nineteen  miles  per  second  ;  and  the  most 
reasonable  supposition  we  can  make,  at  present,  to  ac- 
count for  the  great  velocity  of  the  meteors,  is,  that  they 
derived  a  relative  motion  from  the  earth's  passing  rap- 
idly by  them, — a  supposition  which  is  countenanced  by 
the  fact  that  they  generally  tended  westward  contrary 
to  the  earth's  motion  in  its  orbit. 

In  the  sixth  place,  the  meteors  consisted  of  com- 
bustible matter,  and  took  fire,  and  were  consumed,  in 
traversing  the  atmosphere.  That  these  bodies  under- 
went combustion,  we  had  the  direct  evidence  of  the 
senses,  inasmuch  as  we  saw  them  burn.  That  they 
took  fire  in  the  atmosphere,  was  inferred  from  the  fact 
that  they  were  not  luminous  in  their  original  situations 
in  space,  otherwise,  we  should  have  seen  the  body  from 
which  they  emanated ;  and  had  they  been  luminous 
before  reaching  the  atmosphere,  we  should  have  seen 
them  for  a  much  longer  period  than  they  were  in  sight, 
as  they  must  have  occupied  a  considerable  time  in  de- 
scending towards  the  earth  from  so  great  a  distance, 
even  at  the  rapid  rate  at  which  they  travelled.  The 
immediate  consequence  of  the  prodigious  velocity  with 
which  the  meteors  fell  into  the  atmosphere  must  be  a 
powerful  condensation  of  the  air  before  them,  retarding 
their  progress,  and  producing,  by  a  sudden  compression 
of  the  air,  a  great  evolution  of  heat.  There  is  a  little 
instrument  called  the  air-match,  consisting  of  a  piston 
and  cylinder,  like  a  syringe,  in  which  we  strike  a  light 
by  suddenly  forcing  down  the  piston  upon  the  air  be- 
low. As  the  air  cannot  escape,  it  is  suddenly  com- 
pressed, and  gives  a  spark  sufficient  to  light  a  piece  of 
tinder  at  the  bottom  of  the  cylinder.  Indeed,  it  is  a  well- 


356  LETTERS  ON  ASTRONOMY. 

known  fact,  that,  whenever  air  is  suddenly  and  forci- 
bly compressed,  heat  is  elicited  ;  and,  if  by  such  a  com- 
pression as  may  be  given  by  the  hand  in  the  air-match, 
heat  is  evolved  sufficient  to  fire  tinder,  what  must  be 
the  heat  evolved  by  the  motion  of  a  large  body  in  the 
atmosphere,  with  a  velocity  so  immense.  It  is  com- 
mon to  resort  to  electricity  as  the  agent  which  produces 
the  heat  and  light  of  shooting  stars  ;  but  even  were  elec- 
tricity competent  to  produce  this  effect,  its  presence, 
in  the  case  before  us,  is  not  proved ;  and  its  agency 
is  unnecessary,  since  so  swift  a  motion  of  the  meteors 
themselves,  suddenly  condensing  the  air  before  them, 
is  both  a  known  and  adequate  cause  of  an  intense  light 
and  heat.  A  combustible  body  falling  into  the  atmos- 
phere, under  such  circumstances,  would  become  speedi- 
ly ignited,  but  could  not  burn  freely,  until  it  became 
enveloped  in  air  of  greater  density ;  but,  on  reaching 
the  lower  portions  of  the  atmosphere,  it  would  burn 
with  great  rapidity. 

In  the  seventh  place,  some  of  the  larger  meteors 
must  have  been  bodies  of  great  size.  According  to 
the  testimony  of  various  individuals,  in  different  parts 
of  the  United  States,  a  few  fire-balls  appeared  as  large 
as  the  full  moon.  Dr.  Smith,  (then  of  North  Carolina, 
but  since  surgeon-general  of  the  Texian  army,)  who 
was  travelling  all  night  on  professional  business,  de- 
scribes one  which  he  saw  in  the  following  terms :  "  In 
size  it  appeared  somewhat  larger  than  the  full  moon  ris- 
ing. I  was  startled  by  the  splendid  light  in  which  the 
surrounding  scene  was  exhibited,  rendering  even  small 
objects  quite  visible ;  but  I  heard  no  noise,  although 
every  sense  seemed  to  be  suddenly  aroused,  in  sympa- 
thy with  the  violent  impression  on  the  sight."  This 
description  implies  not  only  that  the  body  was  very 
large,  but  that  it  was  at  a  considerable  distance  from 
the  spectator.  Its  actual  size  will  depend  upon  the  dis- 
tance ;  for,  as  it  appeared  under  the  same  angle  as  the 
moon,  its  diameter  will  bear  the  same  ratio  to  the 
moon's,  as  its  distance  bears  to  the  moon's  distance. 


METEORIC   SHOWERS.  357 

We  could,  therefore,  easily  ascertain  how  large  it  was, 
provided  we  could  find  how  far  it  was  from  the  observ- 
er. If  it  was  one  hundred  and  ten  miles  distant,  its 
diameter  was  one  mile,  and  in  the  same  proportion  for 
a  greater  or  less  distance ;  and,  if  only  at  the  distance 
of  one  mile,  its  diameter  was  forty-eight  feet.  For  a 
moderate  estimate,  we  will  suppose  it  to  have  been 
twenty-two  miles  off;  then  its  diameter  was  eleven 
hundred  and  fifty-six  feet.  Upon  every  view  of  the 
case,  therefore,  it  must  be  admitted,  that  these  were 
bodies  of  great  size,  compared  with  other  objects  which 
traverse  the  atmosphere.  We  may  further  infer  the 
great  magnitude  of  some  of  the  meteors,  from  the  di- 
mensions of  the  trains,  or  clouds,  which  resulted  from 
their  destruction.  These  often  extended  over  several 
degrees,  and  at  length  were  borne  along  in  the  direc- 
tion of  the  wind,  exactly  in  the  manner  of  a  small 
cloud. 

It  was  an  interesting  problem  to  ascertain,  if  possible, 
the  height  above  the  earth  at  which  these  fire-balls  ex- 
ploded, or  resolved  themselves  into  a  cloud  of  smoke. 
This  would  be  an  easy  task,  provided  we  could  be  cer- 
tain that  two  or  more  distant  observers  could  be  sure 
that  both  saw  the  same  meteor ;  for  as  each  would  re- 
fer the  place  of  explosion,  or  the  position  of  the  cloud 
that  resulted  from  it,  to  a  different  point  of  the  sky,  a 
parallax  would  thus  be  obtained,  from  which  the  height 
might  be  determined.  The  large  meteor  which  is  men- 
tioned in  my  account  of  the  shower,  (see  page  348,) 
as  having  exploded  near  the  star  Capella,  was  so  pecu- 
liar in  its  appearance,  and  in  the  form  and  motions  of 
the  small  cloud  which  resulted  from  its  combustion, 
that  it  was  noticed  and  distinguished  by  a  number  of 
observers  in  distant  parts  of  the  country.  All  described 
the  meteor  as  exhibiting,  substantially,  the  same  pecu- 
liarities of  appearance;  all  agreed  very  nearly  in  the 
time  of  its  occurrence ;  and,  on  drawing  lines,  to  rep- 
resent the  course  and  direction  of  the  place  where  it 
exploded  to  the  view  of  each  of  the  observers  respec- 


358  LETTERS  ON  ASTRONOMY. 

tively,  these  lines  met  in  nearly  one  and  the  same  point, 
and  that  was  over  the  place  where  it  was  seen  in  the 
zenith.  Little  doubt,  therefore,  could  remain,  that  all 
saw  the  same  body ;  and  on  ascertaining,  from  a  com- 
parison of  their  observations,  the  amount  of  parallax, 
and  thence  deducing  its  height, — a  task  which  was  ably 
executed  by  Professor  Twining, — the  following  results 
were  obtained :  that  this  meteor,  and  probably  all  the 
meteors,  entered  the  atmosphere  with  a  velocity  not 
less,  but  perhaps  greater,  than  fourteen  miles  in  a  sec- 
ond ;  that  they  became  luminous  many  miles  from  the 
earth, — in  this  case,  over  eighty  miles ;  and  became 
extinct  high  above  the  surface, — in  this  case,  nearly 
thirty  miles. 

In  the  eighth  place,  the  meteors  were  combustible 
bodies,  and  were  constituted  of  light  and  transpa- 
rent materials.  The  fact  that  they  burned  is  sufficient 
proof  that  they  belonged  to  the  class  of  combustible 
bodies ;  and  they  must  have  been  composed  of  very 
light  materials,  otherwise  their  momentum  would  have 
been  sufficient  to  enable  them  to  make  their  way  through 
the  atmosphere  to  the  surface  of  the  earth.  To  com- 
pare great  things  with  small,  we  may  liken  them  to  a 
wad  discharged  from  a  piece  of  artillery,  its  velocity 
being  supposed  to  be  increased  (as  it  may  be)  to  such 
a  degree,  that  it  shall  take  fire  as  it  moves  through  the 
air.  Although  it  would  force  its  way  to  a  great  dis- 
tance from  the  gun,  yet,  if  not  consumed  too  soon,  it 
would  at  length  be  stopped  by  the  resistance  of  the  air. 
Although  it  is  supposed  that  the  meteors  did  in  fact 
slightly  disturb  the  atmospheric  equilibrium,  yet,  had 
they  been  constituted  of  dense  matter,  like  meteoric 
stones,  they  would  doubtless  have  disturbed  it  vastly 
more.  Their  own  momentum  would  be  lost  only  as  it 
was  imparted  to  the  air ;  and  had  such  a  number  of 
bodies, — some  of  them  quite  large,  perhaps  a  mile  in 
diameter,  and  entering  the  atmosphere  with  a  velocity 
more  than  forty  times  the  greatest  velocity  of  a  cannon 
ball,— had  they  been  composed  of  dense,  ponderous 


METEORIC   SHOWERS.  359 

matter,  we  should  have  had  appalling  evidence  of  this 
fact,  not  only  in  the  violent  winds  which  they  would 
have  produced  in  the  atmosphere,  but  in  the  calamities 
they  would  have  occasioned  on  the  surface  of  the 
earth.  The  meteors  were  transparent  bodies ;  other- 
wise, we  cannot  conceive  why  the  body  from  which 
they  emanated  was  not  distinctly  visible,  at  least  by  re- 
flecting the  light  of  the  sun.  If  only  the  meteors  which 
were  known  to  fall  towards  the  earth  had  been  collect- 
ed and  restored  to  their  original  connexion  in  space, 
they  would  have  composed  a  body  of  great  extent ; 
and  we  cannot  imagine  a  body  of  such  dimensions, 
under  such  circumstances,  which  would  not  be  visible, 
unless  formed  of  highly  transparent  materials.  By 
these  unavoidable  inferences  respecting  the  kind  of 
matter  of  which  the  meteors  were  composed,  we  are 
unexpectedly  led  to  recognise  a  body  bearing,  in  its 
constitution,  a  strong  analogy  to  comets,  which  are 
also  composed  of  exceedingly  light  and  transparent, 
and,  as  there  is  much  reason  to  believe,  of  combustible 
matter. 

We  now  arrive  at  the  final  inquiry,  what  relations 
did  the  body  which  afforded  the  meteoric  shower  sus- 
tain to  the  earth  ?  Was  it  of  the  nature  of  a  satellite, 
or  terrestrial  comet,  that  revolves  around  the  earth  as 
its  centre  of  motion  ?  Was  it  a  collection  of  nebulous, 
or  cometary  matter,  which  the  earth  encountered  in  its 
annual  progress  ?  or  was  it  a  comet,  which  chanced  at 
this  time  to  be  pursuing  its  path  along  with  the  earth, 
around  their  common  centre  of  motion  ?  It  could  not 
have  been  of  the  nature  of  a  satellite  to  the  earth,  (or 
one  of  those  bodies  which  are  held  by  some  to  afford 
the  meteoric  stones,  which  sometimes  fall  to  the  earth 
from  huge  meteors  that  traverse  the  atmosphere,)  be- 
cause it  remained  so  long  stationary  with  respect  to  the 
earth.  A  body  so  near  the  earth  as  meteors  of  this 
class  are  known  to  be,  could  not  remain  apparently  sta- 
tionary among  the  stars  for  a  moment;  whereas  the 
body  in  question  occupied  the  same  position,  with 


360  LETTERS  ON  ASTRONOMY. 

hardly  any  perceptible  variation,  for  at  least  two  hours. 
Nor  can  we  suppose  that  the  earth,  in  its  annual  prog- 
ress, came  into  the  vicinity  of  a  nebula,  which  was 
either  stationary,  or  wandering  lawless  through  space. 
Such  a  collection  of  matter  could  not  remain  stationary 
within  the  solar  system,  in  an  insulated  state,  for,  if  not 
prevented  by  a  motion  of  its  own,  or  by  the  attraction 
of  some  nearer  body,  it  would  have  proceeded  directly 
towards  the  sun ;  and  had  it  been  in  motion  in  any 
other  direction  than  that  in  which  the  earth  was  mov- 
ing, it  would  soon  have  been  separated  from  the  earth ; 
since,  during  the  eight  hours,  while  the  meteoric  show- 
er was  visible,  the  earth  moved  in  its  orbit  through  the 
space  of  nearly  five  hundred  and  fifty  thousand  miles. 

The  foregoing  considerations  conduct  us  to  the  fol- 
lowing train  of  reasoning.  First,  if  all  the  meteors 
which  fell  on  the  morning  of  November  13,  1833,  had 
been  collected  and  restored  to  their  original  connexion 
in  space,  they  would  of  themselves  have  constituted  a 
nebulous  body  of  great  extent ;  but  we  have  reason  to 
suppose  that  they,  in  fact,  composed  but  a  small  part 
of  the  mass  from  which  they  emanated,  since,  after  the 
loss  of  so  much  matter  as  proceeded  from  it  in  the 
great  meteoric  shower  of  1799,  and  in  the  several  rep- 
etitions of  it  that  preceded  the  year  1833,  it  was  still 
capable  of  affording  so  copious  a  shower  on  that  year ; 
and  similar  showers,  more  limited  in  extent,  were  re- 
peated for  at  least  five  years  afterwards.  We  are 
therefore  to  regard  the  part  that  descended  only  as  the 
extreme  portions  of  a  body  or  collection  of  meteors, 
of  unknown  extent,  existing  in  the  planetary  spaces. 

Secondly,  since  the  earth  fell  in  with  this  body  in 
the  same  part  of  its  orbit,  for  several  years  in  succes- 
sion, it  must  either  have  remained  there  while  the  earth 
was  performing  its  whole  revolution  around  the  sun,  or 
it  must  itself  have  had  a  revolution,  as  well  as  the  earth. 
But  I  have  already  shown  that  it  could  not  have  re- 
mained stationary  in  that  part  of  space ;  therefore,  it 
must  have  had  a  revolution  around  the  sun. 


METEORIC  SHOWERS.  361 

Thirdly,  its  period  of  revolution  must  have  either 
been  greater  than  the  earth's,  equal  to  it,  or  less.  It 
could  not  have  been  greater,  for  then  the  two  bodies 
could  not  have  been  together  again  at  the  end  of  the 
year,  since  the  meteoric  body  would  not  have  completed 
its  revolution  in  a  year.  Its  period  might  obviously  be 
the  same  as  the  earth's,  for  then  they  might  easily  come 
together  again  after  one  revolution  of  each ;  although 
their  orbits  might  differ  so  much  in  shape  as  to  prevent 
their  being  together  at  any  intermediate  point.  But 
the  period  of  the  body  might  also  be  less  than  that  of 
the  earth,  provided  it  were  some  aliquot  part  of  a  year, 
so  as  to  revolve  just  twice,  or  three  times,  for  example, 
while  the  earth  revolves  once.  Let  us  suppose  that 
the  period  is  one  third  of  a  year.  Then,  since  we 
have  given  the  periodic  times  of  the  two  bodies,  and 
the  major  axis  of  the  orbit  of  one  of  them,  namely,  of 
the  earth,  we  can,  by  Kepler's  law,  find  the  major  axis 
of  the  other  orbit ;  for  the  square  of  the  earth's  peri- 
odic time  I2  is  to  the  square  of  the  body's  time  (|)2 
as  the  cube  of  the  major  axis  of  the  earth's  orbit  is  to 
the  cube  of  the  major  axis  of  the  orbit  in  question. 
Now,  the  three  first  terms  of  this  proportion  are  known, 
and  consequently,  it  is  only  to  solve  a  case  in  the  sim- 
ple rule  of  three,  to  find  the  term  required.  On  mak- 
ing the  calculation,  it  is  found,  that  the  supposition  of 
a  periodic  time  oNmly  one  third  of  a  year  gives  an  or- 
bit of  insufficient  length  ;  the  whole  major  axis  would 
not  reach  from  the  sun  to  the  earth  ;  and  consequently, 
a  body  revolving  in  it  could  never  come  near  to  the 
earth.  On  making  trial  of  six  months,  we  obtain  an  or- 
bit which  satisfies  the  conditions,  being  such  as  is  rep- 
resented by  the  diagram  on  page  362,  Fig.  69',  where 
the  outer  circle  denotes  the  earth's  orbit,  the  sun  being 
in  the  centre,  and  the  inner  ellipse  denotes  the  path  of 
the  meteoric  body.  The  two  bodies  are  together  at 
the  top  of  the  figure,  being  the  place  of  the  meteoric 
body's  aphelion  on  the  thirteenth  of  November,  and 
the  figures  10,  20,  &c.,  denote  the  relative  positions 
31  L.  A. 


362 


LETTERS  ON  ASTRONOM'YV 
Fig.  69'. 


of  the  earth  and  the  body  for  every  ten  days,  for  a  period 
of  six  months,  in  which  time  the  body  would  have  return- 
ed to  its  aphelion. 

Such  would  be  the  relation  of  the  body  that  af- 
fords the  meteoric  shower  of  November,  provided  its 
revolution  is  accomplished  in  six  months ;  but  it  is  still 
somewhat  uncertain  whether  the  period  be  half  a  year 
or  a  year ;  it  must  be  one  or  the  other. 

If  we  inquire,  now,  why  the  meteors  always  appear  to 
radiate  from  a  point  in  the  constellation  Leo,  recollect- 
ing that  this  is  the  point  to  which  the  body  is  projected 


METEORIC  SHOWERS.  363 

among  the  stars,  the  answer  is,  that  this  is  the  very 
point  towards  which  the  earth  is  moving  in  her  orbit 
at  that  time ;  so  that  if,  as  we  have  proved,  the  earth 
passed  through  or  near  a  nebulous  body  on  the  thir- 
teenth of  November,  that  body  must  necessarily  have 
been  projected  into  the  constellation  Leo,  else  it  could 
not  have  lain  directly  in  her  path.  I  consider  it  there- 
fore as  established  by  satisfactory  proof,  that  the  me- 
teors of  November  thirteenth  emanate  from  a  nebulous 
or  cometary  body,  revolving  around  the  sun,  and  com- 
ing so  near  the  earth  at  that  time  that  the  earth  passes 
through  its  skirts,  or  extreme  portions,  and  thus  attracts 
to  itself  some  portions  of  its  matter,  giving  to  the 
meteors  a  greater  velocity  than  could  be  imparted  by 
gravity  alone,  in  consequence  of  passing  rapidly  by 
them. 

All  these  conclusions  were  made  out  by  a  process  of 
reasoning  strictly  inductive,  without  supposing  that  the 
meteoric  body  itself  had  ever  been  seen.  But  there 
are  some  reasons  for  believing  that  we  do  actually  see 
it,  and  that  it  is  no  other  than  that  mysterious  appear- 
ance long  known  under  the  name  of  the  zodiacal  light. 
This  is  a  faint  light,  which  at  certain  seasons  of  the  year 
appears  in  the  west  after  evening  twilight,  and  at  cer- 
tain other  seasons  appears  in  the  east  before  the  dawn, 
following  or  preceding  the  track  of  the  sun  in  a  trian- 
gular figure,  with  its  broad  base  next  to  the  sun,  and 
its  vertex  reaching  to  a  greater  or  less  distance,  some- 
times more  than  ninety  degrees  from  that  luminary. 
You  may  obtain  a  good  view  of  it  in  February  or  March, 
in  the  west,  or  in  October,  in  the  morning  sky.  The 
various  changes  which  this  light  undergoes  at  different 
seasons  of  the  year  are  such  as  to  render  it  probable, 
to  my  mind,  that  this  is  the  very  body  which  affords 
the  meteoric  showers  ;  its  extremity  coming,  in  Novem- 
ber, within  the  sphere  of  the  earth's  attraction.  But, 
as  the  arguments  for  the  existence  of  a  body  in  the 
planetary  regions,  which  affords  these  showers,  were 
drawn  without  the  least  reference  to  the  zodiacal  light, 


364  LETTERS  ON   ASTRONOMY. 

and  are  good,  should  it  finally  be  proved  that  this  light 
has  no  connexion  with  them,  I  will  not  occupy  your 
attention  with  the  discussion  of  this  point,  to  the  ex- 
clusion of  topics  which  will  probably  interest  you  more. 
It  is  perhaps  most  probable,  that  the  meteoric  show- 
ers of  August  and  December  emanate  from  the  same 
body.  I  know  of  nothing  repugnant  to  this  conclusion, 
although  it  has  not  yet  been  distinctly  made  out.  Had 
the  periods  of  the  earth  and  of  the  meteoric  body  been 
so  adjusted  to  each  other  that  the  latter  was  contained 
an  exact  even  number  of  times  in  the  former ;  that  is, 
had  it  been  exactly  either  a  year  or  half  a  year;  then 
we  might  expect  a  similar  recurrence  of  the  meteoric 
shower  every  year ;  but  only  a  slight  variation  in  such 
a  proportion  between  the  two  periods  would  occasion 
the  repetition  of  the  shower  for  a  few  years  in  succes- 
sion, and  then  an  intermission  of  them,  for  an  unknown 
length  of  time,  until  the  two  bodies  were  brought  into 
the  same  relative  situation  as  before.  Disturbances, 
also,  occasioned  by  the  action  of  Venus  and  Mercury, 
might  wholly  subvert  this  numerical  relation,  and  in- 
crease or  diminish  the  probability  of  a  repetition  of  the 
phenomenon.  Accordingly,  from  the  year  1830,  when 
the  meteoric  shower  of  November  was  first  observed, 
until  1833,  there  was  a  regular  increase  of  the  exhibi- 
tion ;  in  1833,  it  came  to  its  maximum;  and  after  that 
time  it  was  repeated  upon  a  constantly  diminishing 
scale,  until  1838,  since  which  time  it  has  not  been  ob- 
served. Perhaps  ages  may  roll  away  before  the  world 
will  be  again  surprised  and  delighted  with  a  display  of 
celestial  fire-works  equal  to  that  of  the  morning  of  No- 
vember 13,  1833. 


FIXED  STARS. 


LETTER  XXVIIL 


FIXED  STARS. 


O,  majestic  Night 


Nature's  great  ancestor  !  Day's  elder  bom, 

And  fated  to  survive  the  transient  sun ! 

By  mortals  and  immortals  seen  with  awe  ! 

A  starry  crown  thy  raven  brow  adorns, 

An  azure  zone  thy  waist  ;  clouds,  in  heaven's  loom 

Wrought,  through  varieties  of  shape  and  shade, 

In  ample  folds  of  drapery  divine, 

Thy  flowing  mantle  form}  and  heaven  throughout 

Voluminously  pour  thy  pompous  train." — Young. 

SINCE  the  solar  system  is  but  one  among  a  myriad  of 
worlds  which  astronomy  unfolds,  it  may  appear  to  you 
that  I  have  dwelt  too  long  on  so  diminutive  a  part  of 
creation,  and  reserved  too  little  space  for  the  other  sys- 
tems of  the  universe.  But  however  humble  a  province 
our  sun  and  planets  compose,  in  the  vast  empire  of 
Jehovah,  yet  it  is  that  which  most  concerns  us  ;  and  it 
is  by  the  study  of  the  laws  by  which  this  part  of  crea- 
tion is  governed,  that  we  learn  the  secrets  of  the  skies. 

Until  recently,  the  observation  and  study  of  the  phe- 
nomena of  the  solar  system  almost  exclusively  occupied 
the  labors  of  astronomers.  But  Sir  William  Herschel 
gave  his  chief  attention  to  the  sidereal  heavens,  and 
opened  new  and  wonderful  fields  of  discovery,  as  well  as 
of  speculation.  The  same  subject  has  been  prosecuted 
with  similar  zeal  and  success  by  his  son,  Sir  John  Her- 
schel, and  Sir  James  South,  in  England,  and  by  Pro- 
fessor Struve,  of  Dorpat,  until  more  has  been  actually 
achieved  than  preceding  astronomers  had  ventured  to 
conjecture.  A  limited  sketch  of  these  wonderful  dis- 
coveries is  all  that  I  propose  to  offer  you. 

The  fixed  stars  are  so  called,  because,  to  common  ob- 
servation, they  always  maintain  the  same  situations  with 
respect  to  one  another.  The  stars  are  classed  by  their 
apparent  magnitudes.  The  whole  number  of  magni- 
tudes recorded  are  sixteen,  of  which  the  first  six  only 
are  visible  to  the  naked  eye;  the  rest  are  telescopic 
31* 


366  LETTERS  ON  ASTRONOMY. 

stars.  These  magnitudes  are  not  determined  by  any 
very  definite  scale,  but  are  merely  ranked  according  to 
their  relative  degrees  of  brightness,  and  this  is  left  in  a 
great  measure  to  the  decision  of  the  eye  alone.  The 
brightest  stars,  to  the  number  of  fifteen  or  twenty,  are 
considered  as  stars  of  the  first  magnitude  ;  the  fifty  or 
sixty  next  brightest,  of  the  second  magnitude  ;  the  next 
two  hundred,  of  the  third  magnitude ;  and  thus  the 
number  of  each  class  increases  rapidly,  as  we  descend 
the  scale,  so  that  no  less  than  fifteen  or  twenty  thous- 
and are  included  within  the  first  seven  magnitudes. 

The  stars  have  been  grouped  in  constellations  from 
the  most  remote  antiquity  ;  a  few,  as  Orion,  Bootes,  and 
Ursa  Major,  are  mentioned  in  the  most  ancient  writings, 
under  the  same  names  as  they  bear  at  present.  The 
names  of  the  constellations  are  sometimes  founded  on 
a  supposed  resemblance  to  the  objects  to  which  they  be- 
long ;  as  the  Swan  and  the  Scorpion  were  evidently 
so  denominated  from  their  likeness  to  those  animals ; 
but  in  most  cases,  it  is  impossible  for  us  to  find  any 
reason  for  designating  a  constellation  by  the  figure  of 
the  animal  or  hero  which  is  employed  to  represent  it. 
These  representations  were  probably  once  blended  with 
the  fables  of  pagan  mythology.  The  same  figures,  ab- 
surd as  they  appear,  are  still  retained  for  the  conven- 
ience of  reference  ;  since  it  is  easy  to  find  any  particu- 
lar star,  by  specifying  the  part  of  the  figure  to  which 
it  belongs ;  as  when  we  say,  a  star  is  in  the  neck  of 
Taurus,  in  the  knee  of  Hercules,  or  in  the  tail  of  the 
Great  Bear.  This  method  furnishes  a  general  clue 
to  its  position  ;  but  the  stars  belonging  to  any  con- 
stellation are  distinguished  according  to  their  apparent 
magnitudes,  as  follows  :  First,  by  the  Greek  letters,  Al- 
pha, Beta,  Gamma,  &c.  Thus,  Alpha  Orionis  denotes 
the  largest  star  in  Orion ;  Beta  Andromeda,  the  sec- 
ond star  in  Andromeda  ;  and  Gamma  Leonis,  the  third 
brightest  star  in  the  Lion.  When  the  number  of  the 
Greek  letters  is  insufficient  to  include  all  the  stars  in  a 
constellation,  recourse  is  had  to  the  letters  of  the  Ro- 


FIXED  STARS.  367 

man  alphabet,  a,  b,  c,  &c. ;  and  in  all  cases  where 
these  are  exhausted  the  final  resort  is  to  numbers. 
This  is  evidently  necessary,  since  the  largest  constella- 
tions contain  many  hundreds  or  even  thousands  of  stars. 
Catalogues  of  particular  stars  have  also  been  published, 
by  different  astronomers,  each  author  numbering  the 
individual  stars  embraced  in  his  list  according  to  the 
places  they  respectively  occupy  in  the  catalogue.  These 
references  to  particular  catalogues  are  sometimes  enter- 
ed on  large  celestial  globes.  Thus  we  meet  with  a  star 
marked  84  H.,  meaning  that  this  is  its  number  in  Her- 
schel's  catalogue ;  or  140  M.,  denoting  the  place  the 
star  occupies  in  the  catalogue  of  Mayer. 

The  earliest  catalogue  of  the  stars  was  made  by 
Hipparchus,  of  the  Alexandrian  school,  about  one  hun- 
dred and  forty  years  before  the  Christian  era.  A  new 
star  appearing  in  the  firmament,  he  was  induced  to 
count  the  stars,  and  to  record  their  positions,  in  order 
that  posterity  might  be  able  to  judge  of  the  permanen- 
cy of  the  constellations.  His  catalogue  contains  all 
that  were  conspicuous  to  the  naked  eye  in  the  latitude 
of  Alexandria,  being  one  thousand  and  twenty-two. 
Most  persons,  unacquainted  with  the  actual  number  of 
the  stars  which  compose  the  visible  firmament,  would 
suppose  it  to  be  much  greater  than  this  ;  but  it  is  found 
that  the  catalogue  of  Hipparchus  embraces  nearly  all 
that  can  now  be  seen  in  the  same  latitude  ;  and  that  on 
the  equator,  where  the  spectator  has  both  the  northern 
and  southern  hemispheres  in  view,  the  number  of  stars 
that  can  be  counted  does  not  exceed  three  thousand. 
A  careless  view  of  the  firmament  in  a  clear  night  gives 
us  the  impression  of  an  infinite  number  of  stars ;  but 
when  we  begin  to  count  them,  they  appear  much  more 
sparsely  distributed  than  we  supposed,  and  large  por- 
tions of  the  sky  appear  almost  destitute  of  stars. 

By  the  aid  of  the  telescope,  new  fields  of  stars  pre- 
sent themselves,  of  boundless  extent ;  the  number  con- 
tinually augmenting,  as  the  powers  of  the  telescope  are 
increased.  Lalande,  in  his  i  Histoire  Celeste/  has  reg- 


368  LETTERS  ON  ASTRONOMY. 

istered  the  positions  of  no  less  than  fifty  thousand  ;  and 
the  whole  number  visible  in  the  largest  telescopes 
amounts  to  many  millions. 

When  you  look  at  the  firmament  on  a  clear  Autum- 
nal or  Winter  evening,  it  appears  so  thickly  studded 
with  stars,  that  you  would  perhaps  imagine  that  the 
task  of  learning  even  the  brightest  of  them  would  be 
almost  hopeless.  Let  me  assure  you,  this  is  all  a  mis- 
take. On  the  contrary,  it  is  a  very  easy  task  to  be- 
come acquainted  with  the  names  and  positions  of  the 
stars  of  the  first  magnitude,  and  of  the  leading  constel- 
lations. If  you  will  give  a  few  evenings  to  the  study, 
you  will  be  surprised  to  find,  both  how  rapidly  you  can 
form  these  new  acquaintances,  and  how  deeply  you 
will  become  interested  in  them.  I  would  advise  you, 
at  first,  to  obtain,  for  an  evening  or  two,  the  assistance 
of  some  friend  who, is  familiar  with  the  stars,  just  to 
point  out  a  few  of  the  most  conspicuous  constellations. 
This  will  put  you  on  the  track,  and  you  will  afterwards 
experience  no  difficulty  in  finding  all  the  constellations 
and  stars  that  are  particularly  worth  knowing ;  espec- 
ially if  you  have  before  you  a  map  of  the  stars,  or,  what 
is  much  better,  a  celestial  globe.  It  is  a  pleasant  even- 
ing recreation  for  a  small  company  of  young  astronomers 
to  go  out  together,  and  learn  one  or  two  constellations 
every  favorable  evening,  until  the  whole  are  mastered. 
If  you  have  a  celestial  globe,  rectify  it  for  the  evening ; 
that  is,  place  it  in  such  a  position,  that  the  constella- 
tions shall  be  seen  on  it  in  the  same  position  with  re- 
spect to  the  horizon,  that  they  have  at  that  moment  in 
the  sky  itself.  To  do  this,  I  first  elevate  the  north 
pole  until  the  number  of  degrees  on  the  brass  meridian 
from  the  pole  to  the  horizon  corresponds  to  my  latitude, 
(forty-one  degrees  and  eighteen  minutes.)  I  then  find 
the  sun's  place  in  the  ecliptic,  by  looking  for  the  day 
of  the  month  on  the  broad  horizon,  and  against  it  no- 
ting the  corresponding  sign  and  degree.  I  now  find 
the  same  sign  and  degree  on  the  ecliptic  itself,  and 
bring  that  point  to  the  brass  meridian.  As  that  will 


FIXED   STARS.  369 

be  the  position  of  the  sun  at  noon,  I  set  the  hour- 
index  at  twelve,  and  then  turn  the  globe  westward, 
until  the  index  points  to  the  given  hour  of  the  eve- 
ning. If  I  now  inspect  the  figures  of  the  constellations, 
and  then  look  upward  at  the  firmament,  I  shall  see 
that  the  latter  are  spread  over  the  sky  in  the  same  man- 
ner as  the  pictures  of  them  are  painted  on  the  globe. 
I  will  point  out  a  few  marks  by  which  the  leading  con- 
stellations may  be  recognised  ;  this  will  aid  you  in  find- 
ing them,  and  you  can  afterwards  learn  the  individual 
stars  of  a  constellation,  to  any  extent  you  please,  by  means 
of  the  globes  or  maps.  Let  us  begin  with  the  Constel- 
lations of  the  Zodiac,  which,  succeeding  each  other, 
as  they  do,  in  a  known  order,  are  most  easily  found. 

Aries  (the  Rani)  is  a  small  constellation,  known  by 
two  bright  stars  which  form  his  head,  Alpha  and  Beta 
Arietis.  These  two  stars  are  about  four  degrees  apart ; 
and  directly  south  of  Beta,  at  the  distance  of  one  de- 
gree, is  a  smaller  star,  Gamma  Jlrietis.  It  has  been 
already  intimated  that  the  Vernal  equinox  probably  was 
near  the  head  of  Aries,  when  the  signs  of  the  zodiac 
received  their  present  names. 

Taurus  (the  Bull)  will  be  readily  found  by  the  sev- 
en stars,  or  Pleiades,  which  lie  in  his  neck.  The  larg- 
est star  in  Taurus  is  Aldebaran,  in  the  Bull's  eye,  a 
star  of  the  first  magnitude,  of  a  reddish  color,  somewhat 
resembling  the  planet  Mars.  Aldebaran  and  four  oth- 
er stars,  close  together  in  the  face  of  Taurus,  compose 
the  Hyades. 

Gemini  (the  Twins)  is  known  by  two  very  bright 
stars,  Castor  and  Pollux,  four  degrees  asunder.  Cas- 
tor (the  northern)  is  of  the  first,  and  Pollux  of  the  sec- 
ond, magnitude. 

Cancer  (the  Crab.)  There  are  no  large  stars  in  this 
constellation,  and  it  is  regarded  as  less  remarkable  than 
any  other  in  the  zodiac.  It  contains,  however,  an  in- 
teresting group  of  small  stars,  called  Praesepe,  or  the 
nebula  of  Cancer,  which  resembles  a  comet,  and  is  of- 
ten mistaken  for  one,  by  persons  unacquainted  with  the 


370  LETTERS  ON  ASTRONOMY. 

stars.  With  a  telescope  of  very  moderate  powers  this 
nebula  is  converted  into  a  beautiful  assemblage  of  ex- 
ceedingly bright  stars. 

Leo  (the  Lion)  is  a  very  large  constellation,  and  has 
many  interesting  members.  Regulus  (Alpha  Leonis) 
is  a  star  of  the  first  magnitude,  which  lies  directly  in 
the  ecliptic,  and  is  much  used  in  astronomical  obser- 
vations. North  of  Regulus,  lies  a  semicircle  of  bright 
stars,  forming  a  sickle,  of  which  Regulus  is  the  handle. 
Denebola,  a  star  of  the  second  magnitude,  is  in  the  Li- 
on's tail,  twenty-five  degrees  northeast  of  Regulus. 

Virgo  (the  Virgin)  extends  a  considerable  way 
from  west  to  east,  but  contains  only  a  few  bright  stars. 
Spied,  however,  is  a  star  of  the  first  magnitude,  and 
lies  a  little  east  of  the  place  of  the  Autumnal  equinox. 
Eighteen  degrees  eastward  of  Denebola,  and  twenty 
degrees  north  of  Spica,  is  Vindemiatrix,  in  the  arm 
of  Virgo,  a  star  of  the  third  magnitude. 

Libra  (the  Balance)  is  distinguished  by  three  large 
stars,  of  which  the  two  brightest  constitute  the  beam  of 
the  balance,  and  the  smallest  forms  the  top  or  handle. 

Scorpio  (the  Scorpion)  is  one  of  the  finest  of  the 
constellations.  His  head  is  formed  of  five  bright  stars, 
arranged  in  the  arc  of  a  circle,  which  is  crossed  in  the 
centre  by  the  ecliptic  nearly  at  right  angles,  near  the 
brightest  of  the  five,  Beta  Scorpionis.  Nine  degrees 
southeast  of  this  is  a  remarkable  star  of  the  first  mag- 
nitude, of  a  reddish  color,  called  Cor  Scorpionis,  or 
Antares.  South  of  this,  a  succession  of  bright  stars 
sweep  round  towards  the  east,  terminating  in  several 
small  stars,  forming  the  tail  of  the  Scorpion. 

Sagittarius  (the  Archer.)  Northeast  of  the  tail  of 
the  Scorpion  are  three  stars  in  the  arc  of  a  circle,  which 
constitute  the  bow  of  the  Archer,  the  central  star  be- 
ing the  brightest,  directly  west  of  which  is  a  bright  star 
which  forms  the  arrow. 

Capricornus  (the  Goat)  lies  northeast  of  Sagittarius, 
and  is  known  by  two  bright  stars,  three  degrees  apart, 
which  form  the  head, 


FIXED  STARS.  371 

Aquarius  (the  Water-Bearer)  is  recognised  by  two 
stars  in  a  line  with  Alpha  Capricorni,  forming  the 
shoulders  of  the  figure.  These  two  stars  are  ten  de- 
grees apart ;  and  three  degrees  southeast  is  a  third  star, 
which,  together  with  the  other  two,  make  an  acute  tri- 
angle, of  which  the  westernmost  is  the  vertex. 

Pisces  (the  Fishes)  lie  between  Aquarius  and  Aries. 
They  are  not  distinguished  by  any  large  stars,  but  are 
connected  by  a  series  of  small  stars,  that  form  a  crook- 
ed line  between  them.  Piscis  Australia,  the  South- 
ern Fish,  lies  directly  below  Aquarius,  and  is  known  by  a 
single  bright  star  far  in  the  south,  having  a  declination 
of  thirty  degrees.  The  name  of  this  star  is  Fomalhaut, 
and  it  is  much  used  in  astronomical  measurements. 

The  constellations  of  the  zodiac,  being  first  well 
learned,  so  as  to  be  readily  recognised,  will  facilitate 
the  learning  of  others  that  lie  north  and  south  of  them. 
Let  us,  therefore,  next  review  the  principal  Northern 
Constellations,  beginning  north  of  Aries,  and  proceed- 
ing from  west  to  east. 

Andromeda  is  characterized  by  three  stars  of  the  sec- 
ond magnitude,  situated  in  a  straight  line,  extending 
from  west  to  east.  The  middle  star  is  about  seventeen 
degrees  north  of  Beta  Arietis.  It  is  in  the  girdle  of 
Andromeda,  and  is  named  Mirach.  The  other  two  lie 
at  about  equal  distances,  fourteen  degrees  west  and  east 
of  Mirach.  The  western  star,  in  the  head  of  Androm- 
eda, lies  in  the  equinoctial  colure.  The  eastern  star, 
Alamak,  is  situated  in  the  foot. 

Perseus  lies  directly  north  of  the  Pleiades,  and  con- 
tains several  bright  stars.  About  eighteen  degrees  from 
the  Pleiades  is  Algol,  a  star  of  the  second  magnitude, 
in  the  head  of  Medusa,  which  forms  a  part  of  the  fig- 
ure ;  and  nine  degrees  northeast  of  Algol  is  Algenib, 
of  the  same  magnitude,  in  the  back  of  Perseus.  Be- 
tween Algenib  and  the  Pleiades  are  three  bright  stars, 
at  nearly  equal  intervals,  which  compose  the  right  leg 
of  Perseus. 

Auriga  (the  Wagoner)  lies  directly  east  of  Perseus, 


372  LETTERS  ON  ASTRONOMY. 

and  extends  nearly  parallel  to  that  constellation,  from 
north  to  south.  Capella,  a  very  white  and  beautiful 
star  of  the  first  magnitude,  distinguishes  this  constella- 
tion. The  feet  of  Auriga  are  near  the  Bull's  horns. 

The  Lynx  comes  next,  but  presents  nothing  partic- 
ularly interesting,  containing  no  stars  above  the  fourth 
magnitude. 

Leo  Minor  consists  of  a  collection  of  small  stars 
north  of  the  sickle  in  Leo,  and  south  of  the  Great  Bear. 
Its  largest  star  is  only  of  the  third  magnitude. 

Coma  Berenices  is  a  cluster  of  small  stars,  north  of 
Denebola,  in  the  tail  of  the  Lion,  and  of  the  head  of 
Virgo.  About  twelve  degrees  directly  north  of  Bere- 
nice's hair,  is  a  single  bright  star,  called  Cor  Caroli,  or 
Charles's  Heart. 

Bootes,  which  comes  next,  is  easily  found  by  means 
of  Arcturus,  a  star  of  the  firs-t  magnitude,  of  a  reddish 
color,  which  is  situated  near  the  knee  of  the  figure. 
Arcturus  is  accompanied  by  three  small  stars,  forming 
a  triangle  a  little  to  the  southwest.  Two  bright  stars, 
Gamma  and  Delta  Bootis,  form  the  shoulders,  and 
Beta,  of  the  third  magnitude,  is  in  the  head,  of  the  figure. 

Corona  Borealis,  (the  Crown,)  which  is  situated 
east  of  Bootes,  is  very  easily  recognised,  composed  as 
it  is  of  a  semicircle  of  bright  stars.  In  the  centre  of  the 
bright  crown  is  a  star  of  the  second  magnitude,  called 
Gemma :  the  remaining  stars  are  all  much  smaller. 

Hercules,  lying  between  the  Crown  on  the  west  and 
the  Lyre  on  the  east,  is  very  thickly  set  with  stars,  most 
of  which  are  quite  small.  This  constellation  covers  a 
great  extent  of  the  sky,  especially  from  north  to  south, 
the  head  terminating  within  fifteen  degrees  of  the  equa- 
tor, and  marked  by  a  star  of  the  third  magnitude,  called 
Ras  Algethi,  which  is  the  largest  in  the  constellation. 

Ophiucus  is  situated  directly  south  of  Hercules,  ex- 
tending some  distance  on  both  sides  of  the  equator,  the 
feet  resting  on  the  Scorpion.  The  head  terminates 
near  the  head  of  Hercules,  and,  like  that,  is  marked  by 
a  bright  star  within  five  degrees  of  Alpha  Herculis, 


FIXED  STARS.  373 

Ophiucus  is  represented  as  holding  in  his  hands  the 
Serpent,  the  head  of  which,  consisting  of  three  bright 
stars,  is  situated  a  little  south  of  the  Crown.  The  folds 
of  the  serpent  will  be  easily  followed  by  a  succession 
of  bright  stars,  which  extend  a  great  way  to  the  east. 

Aquila  (the  Eagle)  is  conspicuous  for  three  bright 
stars  in  its  neck,  of  which  the  central  one,  Altair,  is  a 
very  brilliant  white  star  of  the  first  magnitude.  Anti- 
nous  lies  directly  south  of  the  Eagle,  and  north  of  the 
head  of  Capricornus. 

Delphinus  (the  Dolphin)  is  a  small  but  beautiful 
constellation,  a  few  degrees  east  of  the  Eagle,  and  is 
characterized  by  four  bright  stars  near  to  one  another, 
forming  a  small  rhombic  square.  Another  star  of  the 
same  magnitude,  five  degrees  south,  makes  the  tail. 

Pegasus  lies  between  Aquarius  on  the  southwest  and 
Andromeda  on  the  northeast.  It  contains  but  few  large 
stars.  A  very  regular  square  of  bright  stars  is  composed 
of  Alpha  AndromedcB  and  the  three  largest  stars  in 
Pegasus  ;  namely,  Scheat,  Markab,  and  Algenib.  The 
sides  composing  this  square  are  each  about  fifteen  de- 
grees. Algenib  is  situated  in  the  equinoctial  colure. 

We  may  now  review  the  Constellations  which  sur- 
round the  north  pole,  within  the  circle  of  perpetual  ap- 
parition. 

Ursa  Minor  (the  Little  Bear)  lies  nearest  the  pole.. 
The  pole-star,  Polaris,  is  in  the  extremity  of  the  tail, 
and  is  of  the  third  magnitude.  Three  stars  in  a  straight 
line,  four  degrees  or  five  degrees  apart,  commencing 
with  the  pole-star,  lead  to  a  trapezium  of  four  stars,  and 
the  whole  seven  form  together  a  dipper, — the  trapezium 
being  the  body  and  the  three  stars  the  handle. 

Ursa  Major  (the  Great  Bear)  is  situated  between 
the  pole  and  the  Lesser  Lion,  and  is  usually  recognised 
by  the  figure  of  a  larger  and  more  perfect  dipper  which 
constitutes  the  hinder  part  of  the  animal.  This  has  also 
seven  stars,  four  in  the  body  of  the  Dipper  and  three 
in  the  handle.  All  these  are  stars  of  much  celebrity. 
The  two  in  the  western  side  of  the  Dipper,  Alpha  and 

32  L.  A. 


374  LETTERS  ON  ASTRONOMY. 

Beta,  are  called  Pointers,  on  account  of  their  always 
being  in  a  right  line  with  the  pole-star,  and  therefore 
affording  an  easy  mode  of  finding  that.  The  first  star 
in  the  tail,  next  the  body,  is  named  Alioth,  and  the 
second,  Mizar.  The  head  of  the  Great  Bear  lies  far  to 
the  westward  of  the  Pointers,  and  is  composed  of  nu- 
merous small  stars ;  and  the  feet  are  severally  composed 
of  two  small  stars  very  near  to  each  other. 

Draco  (the  Dragon)  winds  round  between  the  Great 
and  the  Little  Bear ;  and,  commencing  with  the  tail, 
between  the  Pointers  and  the  pole-star,  it  is  easily 
traced  by  a  succession  of  bright  stars  extending  from 
west  to  east.  Passing  under  Ursa  Minor,  it  returns 
westward,  and  terminates  in  a  triangle  which  forms  the 
head  of  Draco,  near  the  feet  of  Hercules,  northwest  of 
Lyra.  Cepheus  lies  eastward  of  the  breast  of  the  Drag- 
on, but  has  no  stars  above  the  third  magnitude. 

Cassiopeia  is  known  by  the  figure  of  a  chair,  com- 
posed of  four  stars  which  form  the  legs,  and  two  which 
form  the  back.  This  constellation  lies  between  Perseus 
and  Cepheus,  in  the  Milky  Way. 

Cygnus  (the  Stvari)  is  situated  also  in  the  Milky 
Way,  some  distance  southwest  of  Cassiopeia,  towards 
the  Eagle.  Three  bright  stars,  which  lie  along  the 
Milky  Way,  form  the  body  and  neck  of  the  Swan,  and 
two  others,  in  a  line  with  the  middle  one  of  the  three, 
one  above  and  one  below,  constitute  the  wings.  This 
constellation  is  among  the  few  that  exhibit  some  resem- 
blance to  the  animals  whose  names  they  bear. 

Lyra  (the  Lyre)  is  directly  west  of  the  Swan,  and 
is  easily  distinguished  by  a  beautiful  white  star  of  the 
first  magnitude,  Alpha  Lyrce. 

The  Southern  Constellations  are  comparatively  few 
in  number.  I  shall  notice  only  the  Whale,  Orion,  the 
Greater  and  Lesser  Dog,  Hydra,  and  the  Crow. 

Cetus  (the  Whale)  is  distinguished  rather  for  its  ex- 
tent than  its  brilliancy,  reaching  as  it  does  through  forty 
degrees  of  longitude,  while  none  of  its  stars,  except  one, 
are  above  the  third  magnitude.  Menkar  (Alpha  Ceti) 


FIXED   STARS.  375 

in  the  mouth,  is  a  star  of  the  second  magnitude ;  and 
several  other  bright  stars,  directly  south  of  Aries,  make 
the  head  and  neck  of  the  Whale.  Mira,  (Omicron 
Ccti,)  in  the  neck  of  the  Whale,  is  a  variable  star. 

Orion  is  one  of  the  largest  and  most  beautiful  of  the 
constellations,  lying  southeast  of  Taurus.  A  cluster  of 
small  stars  forms  the  head  ;  two  large  stars,  Betalgeus 
of  the  first  and  Bellatrix  of  the  second  magnitude, 
make  the  shoulders  ;  three  more  bright  stars  compose 
the  buckler,  and  three  the  sword ;  and  Rigel,  another 
star  of  the  first  magnitude,  makes  one  of  the  feet.  In 
this  constellation  there  are  seventy  stars  plainly  visible 
to  the  naked  eye,  including  two  of  the  first  magnitude, 
four  of  the  second,  and  three  of  the  third. 

Canis  Major  lies  southeast  of  Orion,  and  is  distin- 
guished chiefly  by  its  containing  the  largest  of  the  fixed 
stars,  Sirius. 

Canis  Minor,  a  little  north  of  the  equator,  between 
Canis  Major  and  Gemini,  is  a  small  constellation,  con- 
sisting chiefly  of  two  stars,  of  which,  Procyon  is  of  the 
first  magnitude. 

Hydra  has  its  head  near  Procyon,  consisting  of  a 
number  of  stars  of  ordinary  brightness.  About  fifteen 
degrees  southeast  of  the  head  is  a  star  of  the  second 
magnitude,  forming  the  heart,  (Cor  Hydra;)  and 
eastward  of  this  is  a  long  succession  of  stars  of  the 
fourth  and  fifth  magnitudes,  composing  the  body  and 
tail,  and  reaching  a  few  degrees  south  of  Spica  Virginis. 

Corvus  (the  Crow)  is  represented  as  standing  on 
the  tail  of  Hydra.  It  consists  of  small  stars,  only  three 
of  which  are  as  large  as  the  third  magnitude. 

In  assigning  the  places  of  individual  stars,  I  have  not 
aimed  at  great  precision  ;  but  such  a  knowledge  as  you 
will  acquire  of  the  constellations  and  larger  stars,  by 
nothing  more  even  than  you  can  obtain  from  the  fore- 
going sketch,  will  not  only  add  greatly  to  the  interest 
with  which  you  will  ever  afterwards  look  at  the  starry 
heavens,  but  it  will  enable  you  to  locate  any  phenom- 
enon that  may  present  itself  in  the  nocturnal  sky,  and 


376  LETTERS  ON  ASTRONOMY. 

to  understand  the  position  of  any  object  that  may  be 
described,  by  assigning  its  true  place  among  the  stars ; 
although  I  hope  you  will  go  much  further  than  this 
mere  outline,  in  cultivating  an  actual  acquaintance  with 
the  stars.  Leaving,  now,  these  great  divisions  of  the 
bodies  of  the  firmament,  let  us  ascend  to  the  next 
order  of  stars,  composing  CLUSTERS. 

In  various  parts  of  the  nocturnal  heavens  are  seen 
large  groups  which,  either  by  the  naked  eye,  or  by  the 
aid  of  the  smallest  telescope,  are  perceived  to  consist 
of  a  great  number  of  small  stars.  Such  are  the  Ple- 
iades, Coma  Berenices,  and  Prsesepe,  or  the  Bee-hive, 
in  Cancer.  The  Pleiades,  or  Seven  Stars,  as  they  are 
called,  in  the  neck  of  Taurus,  is  the  most  conspicuous 
cluster.  When  we  look  directly  at  this  group,  we 
cannot  distinguish  more  than  six  stars ;  but  by  turning 
the  eye  sideways  upon  it,  we  discover  that  there  are 
many  more ;  for  it  is  a  remarkable  fact  that  indirect 
vision  is  far  more  delicate  than  direct.  Thus  we  can 
see  the  zodiacal  light  or  a  comet's  tail  much  more  dis- 
tinctly and  better  defined,  if  we  fix  one  eye  on  a  part 
of  the  heavens  at  some  distance  and  turn  the  other 
eye  obliquely  upon  the  object,  than  we  can  by  looking 
directly  towards  it.  Telescopes  show  the  Pleiades  to 
contain  fifty  or  sixty  stars,  crowded  together,  and  appa- 
rently insulated  from  the  other  parts  of  the  heavens. 
Coma,  Berenices  has  fewer  stars,  but  they  are  of  a  larg- 
er class  than  those  which  compose  the  Pleiades.  The 
Bee-hive,  or  Nebula  of  Cancer,  as  it  is  called,  is  one 
of  the  finest  objects  of  this  kind  for  a  small  telescope, 
being  by  its  aid  converted  into  a  rich  congeries  of  shin- 
ing points.  The  head  of  Orion  affords  an  example  of 
another  cluster,  though  less  remarkable  than  those  al- 
ready mentioned.  These  clusters  are  pleasing  objects 
to  the  telescope  ;  and  since  a  common  spyglass  will 
serve  to  give  a  distinct  view  of  most  of  them,  every 
one  may  have  the  power  of  taking  the  view.  But  we 
pass,  now,  to  the  third  order  of  stars,  which  present 
themselves  much  more  obscurely  to  the  gaze  of  the  as- 


Figures  70,  71,  72,  73. 


CLUSTERS  OF  STARS  AND  NEBULA. 


FIXED  STARS.  377 

tronomer,  and  require  large  instruments  for  the  full  de- 
velopement  of  their  wonderful  organization.  These 
are  the  NEBULAE. 

Nebulae  are  faint  misty  appearances  which  are  dimly 
seen  among  the  stars,  resembling  comets,  or  a  speck  of 
fog.  They  are  usually  resolved  by  the  telescope  into 
myriads  of  small  stars;  though  in  some  instances,  no 
powers  of  the  telescope  have  been  found  sufficient  thus 
to  resolve  them.  The  Galaxy  or  Milky  Way,  presents 
a  continued  succession  of  large  nebulae.  The  telescope 
reveals  to  us  innumerable  objects  of  this  kind.  Sir 
William  Herschel  has  given  catalogues  of  two  thousand 
nebulae,  and  has  shown  that  the  nebulous  matter  is  dis- 
tributed through  the  immensity  of  space  in  quantities 
inconceivably  great,  and  in  separate  parcels,  of  all 
shapes  and  sizes,  and  of  all  degrees  of  brightness  be- 
tween a  mere  milky  appearance  and  the  condensed 
light  of  a  fixed  star.  In  fact,  more  distinct  nebulae 
have  been  hunted  out  by  the  aid  of  telescopes  than  the 
whole  number  of  stars  visible  to  the  naked  eye  in  a 
clear  Winter's  night.  Their  appearances  are  extremely 
diversified.  In  many  of  them  we  can  easily  distinguish 
the  individual  stars ;  in  those  apparently  more  remote, 
the  interval  between  the  stars  diminishes,  until  it  be- 
comes quite  imperceptible  ;  and  in  their  faintest  aspect 
they  dwindle  to  points  so  minute,  as  to  be  appropriate- 
ly denominated  star-dust.  Beyond  this,  no  stars  are 
distinctly  visible,  but  only  streaks  or  patches  of  milky 
light.  The  diagram  facing  page  379  represents  a 
magnificent  nebula  in  the  Galaxy.  In  objects  so  dis- 
tant as  the  fixed  stars,  any  apparent  interval  must  de- 
note an  immense  space  ;  and  just  imagine,  yourself  sit- 
uated any  where  within  the  grand  assemblage  of  stars, 
and  a  firmament  would  expand  itself  over  your  head 
like  that  of  our  evening  sky,  only  a  thousand  times 
more  rich  and  splendid. 

Many  of  the  nebulae  exhibit  a  tendency  towards 
a  globular  form,  and  indicate  a  rapid  condensation 
towards  the  centre.  This  characteristic  is  exhibited  in 
32* 


378  LETTERS  ON  ASTRONOMY. 

the  forms  represented  in  Figs.  70  and  71.  We  have 
here  two  specimens  of  nebulae  of  the  nearer  class, 
where  the  stars  are  easily  discriminated.  In  Figs.  72 
and  73  we  have  examples  of  two  others  of  the  remoter 
kind,  one  of  which  is  of  the  variety  called  star-dust. 
These  wonderful  objects,  however,  are  not  confined  to 
the  spherical  form,  but  exhibit  great  varieties  of  figure. 
Sometimes  they  appear  as  ovals ;  sometimes  they  are 
shaped  like  a  fan  ;  and  the  unresolvable  kind  often  affect 
the  most  fantastic  forms.  The  opposite  diagram,  Fig. 
74,  as  well  as  the  preceding,  affords  a  specimen  of  these 
varieties.,  as  given  in  Professor  Nichols's  'Architecture  of 
the  Heavens,'  where  they  are  faithfully  copied  from  the 
papers  of  Herschel,  in  the  '  Philosophical  Transactions.' 

Sir  John  Herschel  has  recently  returned  from  a  resi- 
dence of  five  years  at  the  Cape  of  Good  Hope,  with 
the  express  view  of  exploring  the  hidden  treasures  of 
the  southern  hemisphere.  The  kinds  of  nebulae  are  in 
general  similar  to  those  of  the  northern  hemisphere, 
and  the  forms  are  equally  various  and  singular.  The 
Magellan  Clouds,  two  remarkable  objects  seen  among 
the  stars  of  that  hemisphere,  and  celebrated  among 
navigators,  appeared  to  the  great  telescope  of  Herschel 
(as  we  are  informed  by  Professor  Nichols)  no  longer 
as  simple  milky  spots,  or  permanent  light  flocculi  of 
cloud,  as  they  appear  to  the  unassisted  eye,  but  shone 
with  inconceivable  splendor.  The  Nubecula  Major,  as 
the  larger  object  is  called,  is  a  congeries  of  clusters  of 
stars,  of  irregular  form,  globular  clusters  and  nebulae 
of  various  magnitudes  and  degrees  of  condensation, 
among  which  is  interspersed  a  large  portion  of  irresolv- 
able nebulous  matter^  which  may  be,  and  probably  is, 
star-dust,  but  which  the  power  of  the  twenty-feet  tel- 
escope shows  only  as  a  general  illumination  of  the  field 
of  view,  forming  a  bright  ground  on  which  the  other 
objects  are  scattered.  The  Nubecula  Minor  (the  lesser 
cloud)  exhibited  appearances  similar,  though  inferior  in 
degree. 

It  is  a  grand  idea,  first  conceived  by  Sir  William 


Figure  74. 


VARIOUS   FORMS  OF  NEBUL/E. 


Figure  75. 


A  NEBULA  IN  THE  MILKY  WAY, 


FIXED  STARS.  379 

Herschel,  and  generally  adopted  by  astronomers,  that 
the  whole  Galaxy,  or  Milky  Way,  is  nothing  else  than 
a  nebula,  and  appears  so  extended,  merely  because  it 
happens  to  be  that  particular  nebula  to  which  we  be- 
long. According  to  this  view,  our  sun,  with  his  atten- 
dant planets  and  comets,  constitutes  but  a  single  star 
of  the  Galaxy,  and  our  firmament  of  stars,  or  visible 
heavens,  is  composed  of  the  stars  of  our  nebula  alone. 
An  inhabitant  of  any  of  the  other  nebulae  would  see 
spreading  over  him  a  firmament  equally  spacious,  and 
in  some  cases  inconceivably  more  brilliant. 

It  is  an  exalted  spectacle  to  travel  over  the  Galaxy 
in  a  clear  night,  with  a  powerful  telescope,  with  the 
heart  full  of  the  idea  that  every  star  is  a  world.  Sir 
William  Herschel,  by  counting  the  stars  in  a  single 
field  of  his  telescope,  estimated  that  fifty  thousand  had 
passed  under  his  review  in  a  zone  two  degrees  in 
breadth,  during  a  single  hour's  observation.  Notwith- 
standing the  apparent  contiguity  of  the  stars  which 
crowd  the  Galaxy,  it  is  certain  that  their  mutual  dis- 
tances must  be  inconceivably  great. 

It  is  with  some  reluctance  that  I  leave,  for  the  pres- 
ent, this  fairy  land  of  astronomy ;  but  I  must  not  omit, 
before  bringing  these  Letters  to  a  conclusion,  to  tell 
you  something  respecting  other  curious  and  interesting 
objects  to  be  found  among  the  stars. 

VARIABLE  STARS  are  those  which  undergo  a  periodi- 
cal change  of  brightness.  One  of  the  most  remarka- 
ble is  the  star  Mira,  in  the  Whale,  (Omicron  Ceti.)  It 
appears  once  in  eleven  months,  remains  at  its  greatest 
brightness  about  a  fortnight,  being  then,  on  some  oc- 
casions, equal  to  a  star  of  the  second  magnitude.  It 
then  decreases  about  three  months,  until  it  becomes 
completely  invisible,  and  remains  so  about  five  months, 
when  it  again  becomes  visible,  and  continues  increasing 
during  the  remaining  three  months  of  its  period. 

Another  very  remarkable  variable  star  is  Algol,  (Beta 
Persei.)  It  is  usually  visible  as  a  star  of  the  second 
magnitude,  and  continues  such  for  two  days  and  four- 


380  LETTERS  ON  ASTRONOMY. 

teen  hours,  when  it  suddenly  begins  to  diminish  in  splen- 
dor, and  in  about  three  and  a  half  hours  is  reduced  to 
the  fourth  magnitude.  It  then  begins  again  to  increase, 
and  in  three  and  a  half  hours  more  is  restored  to  its 
usual  brightness,  going  through  all  its  changes  in  less 
than  three  days.  This  remarkable  law  of  variation 
appears  strongly  to  suggest  the  revolution  round  it  of 
some  opaque  body,  which,  when  interposed  between  us 
and  Algol,  cuts  off  a  large  portion  of  its  light.  "  It  is," 
says  Sir  J.  Herschel,  "an  indication  of  a  high  degree 
of  activity  in  regions  where,  but  for  such  evidences,  we 
might  conclude  all  lifeless.  Our  sun  requires  almost 
nine  times  this  period  to  perform  a  revolution  on  its 
axis.  On  the  other  hand,  the  periodic  time  of  an 
opaque  revolving  body,  sufficiently  large,  which  would 
produce  a  similar  temporary  obscuration  of  the  sun, 
seen  from  a  fixed  star,  would  be  less  than  fourteen 
hours."  The  duration  of  these  periods  is  extremely 
various.  While  that  of  Beta  Persei,  above  mentioned, 
is  less  than  three  days,  others  are  more  than  a  year ; 
and  others,  many  years. 

TEMPORARY  STARS  are  new  stars,  which  have  appear- 
ed suddenly  in  the  firmament,  and,  after  a  certain  in- 
terval, as  suddenly  disappeared,  and  returned  no  more. 
It  was  the  appearance  of  a  new  star  of  this  kind,  one 
hundred  and  twenty-five  years  before  the  Christian  era, 
that  prompted  Hipparchus  to  draw  up  a  catalogue  of 
the  stars,  the  first  on  record.  Such,  also,  was  the  star 
which  suddenly  shone  out,  A.  D.  389,  in  the  Eagle,  as 
bright  as  Venus,  and,  after  remaining  three  weeks,  dis- 
appeared entirely.  At  other  periods,  at  distant  intervals, 
similar  phenomena  have  presented  themselves.  Thus 
the  appearance  of  a  star  in  1572  was  so  sudden,  that 
Tycho  Brahe,  returning  home  one  day,  was  surprised  to 
find  a  collection  of  country  people  gazing  at  a  star  which 
he  was  sure  did  not  exist  half  an  hour  before.  It  was 
then  as  bright  as  Sirius,  and  continued  to  increase  until 
it  surpassed  Jupiter  when  brightest,  and  was  visible  at 
mid-day.  In  a  month  it  began  to  diminish ;  and,  in  three 


FIXED   STARS.  381 

months  afterwards,  it  had  entirely  disappeared.  It  has 
been  supposed  by  some  that,  in  a  few  instances,  the 
same  star  has  returned,  constituting  one  of  the  periodical 
or  variable  stars  of  a  long  period.  Moreover,  on  a 
careful  reexamination  of  the  heavens,  and  a  compari- 
son of  catalogues,  many  stars  are  now  discovered  to  be 
missing. 

DOUBLE  STARS  are  those  which  appear  single  to  the 
naked  eye,  but  are  resolved  into  two  by  the  telescope ; 
or,  if  not  visible  to  the  naked  eye,  are  seen  in  the  tel- 
escope so  close  together  as  to  be  recognised  as  objects 
of  this  class.  Sometimes,  three  or  more  stars  are  found 
in  this  near  connexion,  constituting  triple,  or  multiple 
stars.  Castor,  for  example,  when  seen  by  the  naked 
eye,  appears  as  a  single  star,  but  in  a  telescope  even  of 
moderate  powers,  it  is  resolved  into  two  stars,  of  be- 
tween the  third  and  fourth  magnitudes,  within  five  sec- 
onds of  each  other.  These  two  stars  are  nearly  of 
equal  size ;  but  more  commonly,  one  is  exceedingly 
small  in  comparison  with  the  other,  resembling  a  satel- 
lite near  its  primary,  although  in  distance,  in  light,  and 
in  other  characteristics,  each  has  all  the  attributes  of  a 
star,  and  the  combination,  therefore,  cannot  be  that  of 
a  planet  with  a  satellite.  In  most  instances,  also,  the 
distance  between  these  objects  is  much  less  than  five 
seconds  ;  and,  in  many  cases,  it  is  less  than  one  second. 
The  extreme  closeness,  together  with  the  exceeding  mi- 
nuteness, of  most  of  the  double  stars,  requires  the  best 
telescopes  united  with  the  most  acute  powers  of  obser- 
vation. Indeed,  certain  of  these  objects  are  regarded 
as  the  severest  tests  both  of  the  excellence  of  the  instru- 
ments and  of  the  skill  of  the  observer.  The  diagram 
on  page  382,  Fig.  76,  represents  four  double  stars,  as 
seen  with  appropriate  magnifiers.  No.  1,  exhibits  Ep- 
silon  Bootis  with  a  power  of  three  hundred  and  fifty ; 
No.  2,  Rigel,  with  a  power  of  one  hundred  and  thirty ; 
No.  3,  the  Pole-star,  with  a  power  of  one  hundred  ;  and 
No.  4,  Castor,  with  a  power  of  three  hundred. 

Our  knowledge  of  the  double  stars  almost  commenc- 


382  LETTERS  ON  ASTRONOMY. 

1  2          Fig.  76.        3 


ed  with  Sir  William  Herschel,  about  the  year  1780. 
At  the  time  he  began  his  search  for  them,  he  was  ac- 
quainted with  only  four.  Within  five  years  he  discov- 
ered nearly  seven  hundred  double  stars,  and  during 
his  life,  he  observed  no  less  than  twenty-four  hundred. 
In  his  Memoirs,  published  in  the  Philosophical  Trans- 
actions, he  gave  most  accurate  measurements  of  the 
distances  between  the  two  stars,  and  of  the  angle 
which  a  line  joining  the  two  formed  with  a  circle  paral- 
lel to  the  equator.  These  data  would  enable  him,  or 
at  least  posterity,  to  judge  whether  these  minute  bodies 
ever  change  their  position  with  respect  to  each  other. 
Since  1821,  these  researches  have  been  prosecuted, 
with  great  zeal  and  industry,  by  Sir  James  South  and 
Sir  John  Herschel,  in  England  ;  while  Professor  Struve, 
of  Dorpat,  with  the  celebrated  telescope  of  Fraunho- 
fer,  has  published,  from  his  own  observations,  a  cata- 
logue of  three  thousand  double  stars,  the  determination 
of  which  involved  the  distinct  and  most  minute  inspec- 
tion of  at  least  one  hundred  and  twenty  thousand  stars. 
Sir  John  Herschel,  in  his  recent  survey  of  the  southern 
hemisphere,  is  said  to  have  added  to  the  catalogue  of 
double  stars  nearly  three  thousand  more. 

Two  circumstances  add  a  high  degree  of  interest  to 
the  phenomena  of  double  stars :  the  first  is,  that  a  few 
of  them,  at  least,  are  found  to  have  a  revolution  around 
each  other ;  the  second,  that  they  are  supposed  to  af- 
ford the  means  of  ascertaining  the  parallax  of  the  fixed 
stars.  But  I  must  defer  these  topics  till  my  next  Letter. 


FIXED  STARS.  383 


LETTER  XXIX. 

FIXED   STARS  CONTINUED. 

"  O  how  canst  thou  renounce  the  boundless  store 
Of  charms  that  Nature  to  her  votary  yields  ? 
The  warbling  woodland,  the  resounding  shore, 
The  pomp  of  groves,  and  garniture  of  fields  ; 
All  that  the  genial  ray  of  morning  yields, 
And  all  that  echoes  to  the  song  of  even, 
All  that  the  mountain's  sheltering  bosom  shields, 
And  all  the  dread  magnificence  of  heaven,— 
O  how  canst  thou  renounce,  and  hope  to  be  forgiven  !" — Beattie. 

IN  1803,  Sir  William  Herschel  first  determined  and 
announced  to  the  world,  that  there  exist  among  the  stars 
separate  systems,  composed  of  two  stars  revolving  about 
each  other  in  regular  orbits.  These  he  denominated 
binary  stars,  to  distinguish  them  from  other  double 
stars  where  no  such  motion  is  detected,  and  whose 
proximity  to  each  other  may  possibly  arise  from  casual 
juxtaposition,  or  from  one  being  in  the  range  of  the 
other.  Between  fifty  and  sixty  instances  of  changes, 
to  a  greater  or  less  amount,  of  the  relative  positions  of 
double  stars,  are  mentioned  by  Sir  William  Herschel ; 
and  a  few  of  them  had  changed  their  places  so  much, 
within  twenty-five  years,  and  in  such  order,  as  to  lead 
him  to  the  conclusion  that  they  performed  revolutions, 
one  around  the  other,  in  regular  orbits.  These  conclu- 
sions have  been  fully  confirmed  by  later  observers ;  so 
that  it  is  now  considered  as  fully  established,  that  there 
exist  among  the  fixed  stars  binary  systems,  in  which  two 
stars  perform  to  each  other  the  office  of  sun  and  planet, 
and  that  the  periods  of  revolution  of  more  than  one 
such  pair  have  been  ascertained  with  some  degree  of 
exactness.  Immersions  and  emersions  of  stars  behind 
each  other  have  been  observed,  and  real  motions  among 
them  detected,  rapid  enough  to  become  sensible  and 
measurable  in  very  short  intervals  of  time.  The  peri- 
ods of  the  double  stars  are  very  various,  ranging,  in  the 
case  of  those  already  ascertained,  from  forty-three  years 


384  LETTERS   ON  ASTRONOMY. 

to  one  thousand.  Their  orbits  are  very  small  ellipses, 
only  a  few  seconds  in  the  longest  direction,  and  more 
eccentric  than  those  of  the  planets.  A  double  star  in 
the  Northern  Crown  (Eta  Coronet)  has  made  a  com- 
plete revolution  since  its  first  discovery,  and  is  now  far 
advanced  in  its  second  period ;  while  a  star  in  the  Lion 
(Gamma  Leonis)  requires  twelve  hundred  years  to 
complete  its  circuit. 

You  may  not  at  once  see  the  reason  why  these  revo- 
lutions of  one  member  of  a  double  star  around  the  other, 
should  be  deemed  facts  of  such  extraordinary  interest ; 
to  you  they  may  appear  rather  in  the  light  of  astronom- 
ical curiosities.  But  remark,  that  the  revolutions  of  the 
binary  stars  have  assured  us  of  this  most  interesting  fact, 
that  the  law  of  gravitation  extends  to  the  fixed  stars. 
Before  these  discoveries,  we  could  not  decide,  except 
by  a  feeble  analogy,  that  this  law  transcended  the 
bounds  of  the  solar  system.  Indeed,  our  belief  of  the 
fact  rested  more  upon  our  idea  of  unity  of  design  in  the 
works  of  the  Creator,  than  upon  any  certain  proof ;  but 
the  revolution  of  one  star  around  another,  in  obedience 
to  forces  which  are  proved  to  be  similar  to  those  which 
govern  the  solar  system,  establishes  the  grand  conclu- 
sion, that  the  law  of  gravitation  is  truly  the  law  of  the 
material  universe.  "  We  have  the  same  evidence," 
says  Sir  John  Herschel,  "  of  the  revolutions  of  the  bi- 
nary stars  about  each  other,  that  we  have  of  those  of 
Saturn  and  Uranus  about  the  sun  ;  and  the  correspond- 
ence between  their  calculated  and  observed  places,  in 
such  elongated  ellipses,  must  be  admitted  to  carry  with 
it  a  proof  of  the  prevalence  of  the  Newtonian  law  of 
gravity  in  their  systems,  of  the  very  same  nature  and 
cogency  as  that  of  the  calculated  and  observed  places  of 
comets  round  the  centre  of  our  own  system.  But  it  is 
not  with  the  revolution  of  bodies  of  a  cometary  or  plan- 
etary nature  round  a  solar  centre,  that  we  are  now 
concerned  ;  it  is  with  that  of  sun  around  sun,  each,  per- 
haps, accompanied  with  its  train  of  planets  and  their 
satellites,  closely  shrouded  from  our  view  by  the  splen- 


FIXED  STARS.  385 

dor  of  their  respective  suns,  and  crowded  into  a  space, 
bearing  hardly  a  greater  proportion  to  the  enormous 
interval  which  separates  them,  than  the  distances  of 
the  satellites  of  our  planets  from  their  primaries  bear  to 
their  distances  from  the  sun  itself." 

Many  of  the  double  stars  are  of  different  colors  ;  and 
Sir  John  Herschel  is  of  the  opinion  that  there  exist  in 
nature  suns  of  different  colors.  "  It  may,"  says  he,  "  be 
easier  suggested  in  words  than  conceived  in  imagina- 
tion, what  variety  of  illumination  two  suns,  a  red  and 
a  green,  or  a  yellow  and  a  blue  one,  must  afford  to  a 
planet  circulating  about  either ;  and  what  charming 
contrasts  and  '  grateful  vicissitudes'  a  red  and  a  green 
day,  for  instance,  alternating  with  a  white  one  and  with 
darkness,  might  arise  from  the  presence  or  absence  of 
one  or  other  or  both  above  the  horizon.  Insulated  stars 
of  a  red  color,  almost  as  deep  as  that  of  blood,  occur  in 
many  parts  of  the  heavens ;  but  no  green  or  blue  star, 
of  any  decided  hue,  has  ever  been  noticed  unassociated 
with  a  companion  brighter  than  itself." 

Beside  these  revolutions  of  the  binary  stars,  some  of 
the  fixed  stars  appear  to  have  a  real  motion  in  space. 
There  are  several  apparent  changes  of  pkee  among  the 
stars,  arising  from  real  changes  in  the  earth,  which,  as 
we  are  not  conscious  of  them,  we  refer  to  the  stars ;  but 
there  are  other  motions  among  the  stars  which  cannot 
result  from  any  changes  in  the  earth,  but  must  arise 
from  changes  in  the  stars  themselves.  Such  motions 
are  called  the  proper  motions  of  the  stars.  Nearly  two 
thousand  years  ago,  Hipparchus  and  Ptolemy  made  the 
most  accurate  determinations  in  their  power  of  the  rel- 
ative situations  of  the  stars,  and  their  observations  have 
been  transmitted  to  us  in  Ptolemy's  (  Almagest ;'  from 
which  it  appears  that  the  stars  retain  at  least  very  near- 
ly the  same  places  now  as  they  did  at  that  period. 
Still,  the  more  accurate  methods  of  modern  astronomers 
have  brought  to  light  minute  changes  in  the  places  of 
certain  stars,  which  force  upon  us  the  conclusion,  either 
that  our  solar  system  causes  an  apparent  displacement 
33  L.  A. 


386  LETTERS  ON  ASTRONOMY. 

of  certain  stars,  by  a  motion  of  its  own  in  space,  of 
that  they  have  themselves  a  proper  motion.  Possibly, 
indeed,  both  these  causes  may  operate. 

If  the  sun,  and  of  course  the  earth  which  accompa- 
nies him,  is  actually  in  motion,  the  fact  may  become 
manifest  from  the  apparent  approach  of  the  stars  in  the 
region  which  he  is  leaving,  and  the  recession  of  those 
which  lie  in  the  part  of  the  heavens  towards  which  he  is 
travelling.  Were  two  groves  of  trees  situated  on  a 
plain  at  some  distance  apart,  and  we  should  go  from  one 
to  the  other,  the  trees  before  us  would  gradually  appear 
further  and  further  asunder,  while  those  we  left  behind 
would  appear  to  approach  each  other.  Some  years 
since,  Sir  William  Herschel  supposed  he  had  detected 
changes  of  this  kind  among  two  sets  of  stars  in  opposite 
points  of  the  heavens,  and  announced  that  the  solar  sys- 
tem was  in  motion  towards  a  point  in  the  constellation 
Hercules ;  but  other  astronomers  have  not  found  the 
changes  in  question  such  as  would  correspond  to  this 
motion,  or  to  any  motion  of  the  sun ;  and,  while  it  is  a 
matter  of  general  belief  that  the  sun  has  a  motion  in 
space,  the  fact  is  not  considered  as  yet  entirely  proved. 

In  most  cases,  where  a  proper  motion  in  certain  stars 
has  been  suspected,  its  annual  amount  has  been  so 
small,  that  many  years  are  required  to  assure  us,  that 
the  effect  is  not  owing  to  some  other  cause  than  a  real 
progressive  motion  in  the  stars  themselves  ;  but  in  a  few 
instances  the  fact  is  too  obvious  to  admit  of  any  doubt. 
Thus,  the  two  stars,  61  Cygni,  which  are  nearly  equal, 
have  remained  constantly  at  the  same  or  nearly  at  the 
same  distance  of  fifteen  seconds,  for  at  least  fifty  years 
past.  Mean-while,  they  have  shifted  their  local  situation 
in  the  heavens  four  minutes  twenty-three  seconds,  the 
annual  proper  motion  of  each  star  being  five  seconds 
and  three  tenths,  by  which  quantity  this  system  is  every 
year  carried  along  in  some  unknown  path,  by  a  motion 
which  for  many  centuries  must  be  regarded  as  uniform 
and  rectilinear.  A  greater  proportion  of  the  double 
stars  than  of  any  other  indicate  proper  motions,  espec- 


FIXED  STARS.  387 

ially  the  binary  stars,  or  those  which  have  a  revolution 
around  each  other.  Among  stars  not  double,  and  no 
way  differing  from  the  rest  in  any  other  obvious  partic- 
ular, a  star  in  the  constellation  Cassiopeia,  (Mu  Cassi- 
opeia) has  the  greatest  proper  motion  of  any  yet  ascer- 
tained, amounting  to  nearly  four  seconds  annually. 

You  have  doubtless  heard  much  respecting  the  "  im- 
measurable distances"  of  the  fixed  stars,  and  will  desire 
to  learn  what  is  known  to  astronomers  respecting  this 
interesting  subject. 

We  cannot  ascertain  the  actual  distance  of  any  of 
the  fixed  stars,  but  we  can  certainly  determine  that 
the  nearest  star  is  more  than  twenty  millions  of  mil- 
lions of  miles  from  the  earth,  (20,000,000,000,000.) 
For  all  measurements  relating  to  the  distances  of  the 
sun  and  planets,  the  radius  of  the  earth  furnishes  the 
base  line.  The  length  of  this  line  being  known,  and 
the  horizontal  parallax  of  the  sun  or  any  planet,  we 
have  the  means  of  calculating  the  distance  of  the  body 
from  us,  by  methods  explained  in  a  previous  Letter. 
But  any  star,  viewed  from  the  opposite  sides  of  the 
earth,  would  appear  from  both  stations  to  occupy  pre- 
cisely the  same  situation  in  the  celestial  sphere,  and  of 
course  it  would  exhibit  no  horizontal  parallax.  But  as- 
tronomers have  endeavored  to  find  a  parallax  in  some 
of  the  fixed  stars,  by  taking  the  diameter  of  the  earth's 
orbit  as  a  base  line.  Yet  even  a  change  of  position 
amounting  to  one  hundred  and  ninety  millions  of  miles 
proved,  until  very  recently,  insufficient  to  alter  the 
place  of  a  single  star,  so  far  as  to  be  capable  of  detec- 
tion by  very  refined  observations ;  from  which  it  was 
concluded  that  the  stars  have  not  even  any  annual  par- 
allax ;  that  is,  the  angle  subtended  by  the  semidiameter 
of  the  earth's  orbit,  at  the  nearest  fixed  star,  is  insensi- 
ble. The  errors  to  which  instrumental  measurements 
are  subject,  arising  from  the  defects  of  instruments  them- 
selves, from  refraction,  and  from  various  other  sources 
of  inaccuracy,  are  such,  that  the  angular  determinations 
of  arcs  of  the  heavens  cannot  be  relied  on  to  less  than 


388  LETTERS  ON  ASTRONOMY. 

one  second,  and  therefore  cannot  be  appreciated  by  di- 
rect measurement.  It  follows,  that,  when  viewed  from 
the  nearest  star,  the  diameter  of  the  earth's  orbit  would 
be  insensible ;  the  spider-line  of  the  telescope  would 
more  than  cover  it.  Taking,  however,  the  annual  par- 
allax of  a  fixed  star  at  one  second,  it  can  be  demon- 
strated, that  the  distance  of  the  nearest  fixed  star  must 
exceed  95000000X200000=190000000X100000,  or 
one  hundred  thousand  times  one  hundred  and  ninety 
millions  of  miles.  Of  a  distance  so  vast  we  can  form 
no  adequate  conceptions,  and  even  seek  to  measure  it 
only  by  the  time  that  light  (which  moves  more  than  one 
hundred  and  ninety-two  thousand  miles  per  second,  and 
passes  from  the  sun  to  the  earth  in  eight  minutes  and 
seven  seconds)  would  take  to  traverse  it,  which  is  found 
to  be  more  than  three  and  a  half  years. 

If  these  conclusions  are  drawn  with  respect  to  the 
largest  of  the  fixed  stars,  which  we  suppose  to  be  vastly 
nearer  to  us  than  those  of  the  smallest  magnitude,  the 
idea  of  distance  swells  upon  us  when  we  attempt  to  es- 
timate the  remoteness  of  the  latter.  As  it  is  uncertain, 
however,  whether  the  difference  in  the  apparent  mag- 
nitudes of  the  stars  is  owing  to  a  real  difference,  or 
merely  to  their  being  at  various  distances  from  the  eye, 
more  or  less  uncertainty  must  attend  all  efforts  to  deter- 
mine the  relative  distances  of  the  stars ;  but  astrono- 
mers generally  believe,  that  the  lower  orders  of  stars  are 
vastly  more  distant  from  us  than  the  higher.  Of  some 
stars  it  is  said,  that  thousands  of  years  would  be  requir- 
ed for  their  light  to  travel  down  to  us. 

I  have  said  that  the  stars  have  always  been  held,  un- 
til recently,  to  have  no  annual  parallax ;  yet  it  may  be 
observed  that  astronomers  were  not  exactly  agreed  on 
this  point.  Dr.  Brinkley,  a  late  eminent  Irish  astrono- 
mer, supposed  that  he  had  detected  an  annual  parallax  in 
Alpha  Lyrae,  amounting  to  one  second  and  thirteen  hun- 
dreths,  and  in  Alpha  Aquilae,  of  one  second  and  forty- 
two  hundreths.  These  results  were  controverted  by  Mr. 
Pond,  of  the  Royal  Observatory  of  Greenwich ;  and 


FIXED  STARS.  389 

Mr.  Struve,  of  Dorpat,  has  shown  that,  in  a  number  of 
cases,  the  supposed  parallax  is  in  a  direction  opposite  to 
that  which  would  arise  from  the  motion  of  the  earth. 
Hence  it  is  considered  doubtful  whether,  in  all  cases  of 
an  apparent  parallax,  the  effect  is  not  wholly  due  to  er- 
rors of  observation. 

But  as  if  nothing  was  to  be  hidden  from  our  times, 
the  long  sought  for  parallax  among  the  fixed  stars  has 
at  length  been  found,  and  consequently  the  distance  of 
some  of  these  bodies,  at  least,  is  no  longer  veiled  in 
mystery.  In  the  year  1838,  Professor  Bessel,  of  K6- 
ningsberg,  announced  the  discovery  of  a  parallax  in  one 
of  the  stars  of  the  Swan,  (61  Cygni,)  amounting  to 
about  one  third  of  a  second.  This  seems,  indeed,  so 
small  an  angle,  that  we  might  have  reason  to  suspect 
the  reality  of  the  determination ;  but  the  most  compe- 
tent judges  who  have  thoroughly  examined  the  process 
by  which  the  discovery  was  made,  assent  to  its  validity. 
What,  then,  do  astronomers  understand,  when  they  say 
that  a  parallax  has  been  discovered  in  one  of  the  fixed 
stars,  amounting  to  one  third  of  a  second  ?  They  mean 
that  the  star  in  question  apparently  shifts  its  place  in  the 
heavens,  to  that  amount,  when  viewed  at  opposite  ex- 
tremities of  the  earth's  orbit,  namely,  at  points  in  space 
distant  from  each  other  one  hundred  and  ninety  mil- 
lions of  miles.  On  calculating  the  distance  of  the  star 
from  us  from  these  data,  it  is  found  to  be  six  hundred 
and  fifty-seven  thousand  seven  hundred  times  ninety- 
five  millions  of  miles, — a  distance  which  it  would  take 
light  more  than  ten  years  to  traverse. 

Indirect  methods  have  been  proposed,  for  ascertain- 
ing the  parallax  of  the  fixed  stars,  by  means  of  observa- 
tions on  the  double  stars.  If  the  two  stars  composing 
a  double  star  are  at  different  distances  from  us,  paral- 
lax would  affect  them  unequally,  and  change  their  rel- 
ative positions  with  respect  to  each  other ;  and  since 
the  ordinary  sources  of  error  arising  from  the  im- 
perfection of  instruments,  from  precession,  and  from 
refraction,  would  be  avoided,  (as  they  would  affect 
33* 


390  LETTERS  ON  ASTRONOMY. 

both  objects  alike,  and  therefore  would  not  disturb 
their  relative  positions,)  measurements  taken  with  the 
micrometer  of  changes  much  less  than  one  second  may 
be  relied  on.  Sir  John  Herschel  proposed  a  method, 
by  which  changes  may  be  determined  that  amount  to 
only  one  fortieth  of  a  second. 

The  immense  distance  of  the  fixed  stars  is  inferred 
also  from  the  fact,  that  the  largest  telescopes  do  not  in- 
crease their  apparent  magnitude.  They  are  still  points, 
when  viewed  with  glasses  that  magnify  five  thousand 
times. 

With  respect  to  the  NATURE  OF  THE  STARS,  it  would 
seem  fruitless  to  inquire  into  the  nature  of  bodies  so  dis- 
tant, and  which  reveal  themselves  to  us  only  as  shin- 
ing points  in  space.  Still,  there  are  a  few  very  satis- 
factory inferences  that  can  be  made  out  respecting 
them.  First,  the  fixed  stars  are  bodies  greater  than 
our  earth.  If  this  were  not  the  case,  they  would  not 
be  visible  at  such  an  immense  distance.  Dr.  Wollaston, 
a  distinguished  English  philosopher,  attempted  to  esti- 
mate the  magnitudes  of  certain  of  the  fixed  stars  from 
the  light  which  they  afford.  By  means  of  an  accurate 
photometer,  (an  instrument  for  measuring  the  relative 
intensities  of  light,)  he  compared  the  light  of  Sirius 
with  that  of  the  sun.  He  next  inquired  how  far  the 
sun  must  be  removed  from  us,  in  order  to  appear  no 
brighter  than  Sirius.  He  found  the  distance  to  be  one 
hundred  and  forty-one  thousand  times  its  present  dis- 
tance. But  Sirius  is  more  than  two  hundred  thousand 
times  as  far  off  as  the  sun  ;  hence  he  inferred  that, 
upon  the  lowest  computation,  it  must  actually  give 
out  twice  as  much  light  as  the  sun ;  or  that,  in  point 
of  splendor,  Sirius  must  be  at  least  equal  to  two  suns. 
Indeed,  he  has  rendered  it  probable,  that  its  light  is 
equal  to  that  of  fourteen  suns.  There  is  reason,  how- 
ever, to  believe  that  the  stars  are  actually  of  various 
magnitudes,  and  that  their  apparent  difference  is  not 
owing  merely  to  their  different  distances.  Bessel  es- 
timates the  quantity  of  matter  in  the  two  members  of  a 


FIXED  STARS.  391 

double  star  in  the  Swan,  as  less  than  half  that  of  the 
sun. 

Secondly,  the  fixed  stars  are  suns.  We  have  al- 
ready seen  that  they  are  large  bodies ;  that  they  are 
immensely  further  off  than  the  furthest  planet ;  that 
they  shine  by  their  own  light ;  in  short,  that  their  ap- 
pearance is,  in  all  respects,  the  same  as  the  sun  would 
exhibit  if  removed  to  the  region  of  the  stars.  Hence 
we  infer  that  they  are  bodies  of  the  same  kind  with 
the  sun.  We  are  justified,  therefore,  by  a  sound  anal- 
ogy, in  concluding  that  the  stars  were  made  for  the 
same  end  as  the  sun,  namely,  as  the  centres  of  attrac- 
tion to  other  planetary  worlds,  to  which  they  severally 
dispense  light  and  heat.  Although  the  starry  heavens 
present,  in  a  clear  night,  a  spectacle  of  unrivalled  gran- 
deur and  beauty,  yet  it  must  be  admitted  that  the  chief 
purpose  of  the  stars  could  not  have  been  to  adorn  the 
night,  since  by  far  the  greater  part  of  them  are  invisible 
to  the  naked  eye ;  nor  as  landmarks  to  the  navigator, 
for  only  a  very  small  proportion  of  them  are  adapted 
to  this  purpose ;  nor,  finally,  to  influence  the  earth  by 
their  attractions,  since  their  distance  renders  such  an 
effect  entirely  insensible.  If  they  are  suns,  and  if  they 
exert  no  important  agencies  upon  our  world,  but  are 
bodies  evidently  adapted  to  the  same  purpose  as  our 
sun,  then  it  is  as  rational  to  suppose  that  they  were 
made  to  give  light  and  heat,  as  that  the  eye  was  made 
for  seeing  and  the  ear  for  hearing.  It  is  obvious  to  in- 
quire, next,  to  what  they  dispense  these  gifts,  if  not  to 
planetary  worlds ;  and  why  to  planetary  worlds,  if  not 
for  the  use  of  percipient  beings  ?  We  are  thus  led,  al- 
most inevitably,  to  the  idea  of  a  plurality  of  worlds  ; 
and  the  conclusion  is  forced  upon  us,  that  the  spot 
which  the  Creator  has  assigned  to  us  is  but  a  humble 
province  in  his  boundless  empire. 


392  LETTERS  ON  ASTRONOMY. 


LETTER  XXX. 

SYSTEM    OF    THE    WORLD. 

"  O  how  unlike  the  complex  works  of  man, 
Heaven's  easy,  artless,  unincumbered,  plan." — Coivper. 

HAVING  now  explained  to  you,  as  far  as  I  am  able 
to  do  it  in  so  short  a  space,  the  leading  phenomena  of 
the  heavenly  bodies,  it  only  remains  to  inform  you  of 
the  different  systems  of  the  world  which  have  prevail- 
ed in  different  ages, — a  subject  which  will  necessarily 
involve  a  sketch  of  the  history  of  astronomy. 

By  a  system  of  the  world,  I  understand  an  explana- 
tion of  the  arrangement  of  all  the  bodies  that  compose 
the  material  universe,  and  of  their  relations  to  each  oth- 
er. It  is  otherwise  called  the  '  Mechanism  of  the  Heav- 
ens ;'  and  indeed,  in  the  system  of  the  world,  we  figure 
to  ourselves  a  machine,  all  parts  of  which  have  a  mutual 
dependence,  and  conspire  to  one  great  end.  "The 
machines  that  were  first  invented,"  says  Adam  Smith, 
"  to  perform  any  particular  movement,  are  always  the 
most  complex  ;  and  succeeding  artists  generally  discover 
that,  with  fewer  wheels,  and  with  fewer  principles  of 
motion,  than  had  originally  been  employed,  the  same 
effects  may  be  more  easily  produced.  The  first  sys- 
tems, in  the  same  manner,  are  always  the  most  complex  ; 
and  a  particular  connecting  chain  or  principle  is  gener- 
rally  thought  necessary,  to  unite  every  two  seemingly 
disjointed  appearances ;  but  it  often  happens,  that  one 
great  connecting  principle  is  afterwards  found  to  be 
sufficient  to  bind  together  all  the  discordant  phenomena 
that  occur  in  a  whole  species  of  things  !"  This  remark 
is  strikingly  applicable  to  the  origin  and  progress  of  sys- 
tems of  astronomy.  It  is  a  remarkable  fact  in  the  his- 
tory of  the  human  mind,  that  astronomy  is  the  oldest 
of  the  sciences,  having  been  cultivated,  with  no  small 
success,  long  before  any  attention  was  paid  to  the  causes 


SYSTEM  OF  THE  WORLD.  393 

of  the  common  terrestrial  phenomena.  The  opinion 
has  always  prevailed  among  those  who  were  unenlight- 
ened by  science,  that  very  extraordinary  appearances 
in  the  sky,  as  comets,  fiery  meteors,  and  eclipses,  are 
omens  of  the  wrath  of  heaven.  They  have,  therefore, 
in  all  ages,  been  watched  with  the  greatest  attention : 
and  their  appearances  have  been  minutely  recorded  by 
the  historians  of  the  times.  The  idea,  moreover,  that 
the  aspects  of  the  stars  are  connected  with  the  destinies 
of  individuals  and  of  empires,  has  been  remarkably 
prevalent  from  the  earliest  records  of  history  down  to  a 
very  late  period,  and,  indeed,  still  lingers  among  the 
uneducated  and  credulous.  This  notion  gave  rise  to 
ASTROLOGY, — an  art  which  professed  to  be  able,  by  a 
knowledge  of  the  varying  aspects  of  the  planets  and 
stars,  to  penetrate  the  veil  of  futurity,  and  to  foretel  ap- 
proaching irregularities  of  Nature  herself,  and  the  for- 
tunes of  kingdoms  and  of  individuals.  That  department 
of  astrology  which  took  cognizance  of  extraordinary 
occurrences  in  the  natural  world,  as  tempests,  earth- 
quakes, eclipses,  and  volcanoes,  both  to  predict  their 
approach  and  to  interpret  their  meaning,  was  called 
natural  astrology :  that  which  related  to  the  fortunes 
of  men  and  of  empires,  judicial  astrology.  Among 
many  ancient  nations,  astrologers  were  held  in  the  high- 
est estimation,  and  were  kept  near  the  persons  of  mon- 
archs ;  and  the  practice  of  the  art  constituted  a  lucra- 
tive profession  throughout  the  middle  ages.  Nor  were 
the  ignorant  and  uneducated  portions  of  society  alone 
the  dupes  of  its  pretensions.  Hippocrates,  the  c  Father 
of  Medicine,'  ranks  astrology  among  the  most  important 
branches  of  knowledge  to  the  physician ;  and  Tycho 
Brahe,  and  Lord  Bacon,  were  firm  believers  in  its  mys- 
teries. Astrology,  fallacious  as  it  was,  must  be  acknowl- 
edged to  have  rendered  the  greatest  services  to  astron- 
omy, by  leading  to  the  accurate  observation  and  diligent 
study  of  the  stars. 

At  a  period  of  very  remote  antiquity,  astronomy  was 
cultivated  in  China,  India,  Chaldea,  and  Egypt.     The 


394  LETTERS  ON  ASTRONOMY. 

Chaldeans  were  particularly  distinguished  for  the  accu- 
racy and  extent  of  their  astronomical  observations.  Ca- 
listhenes,  the  Greek  philosopher  who  accompanied  Al- 
exander the  Great  in  his  Eastern  conquests,  transmitted 
to  Aristotle  a  series  of  observations  made  at  Babylon 
nineteen  centuries  before  the  capture  of  that  city  by 
Alexander  ;  and  the  wise  men  of  Babylon  and  the  Chal- 
dean astrologers  are  referred  to  in  the  Sacred  Writings. 
They  enjoyed  a  clear  sky  and  a  mild  climate,  and  their 
pursuits  as  shepherds  favored  long-continued  observa- 
tions ;  while  the  admiration  and  respect  accorded  to 
the  profession,  rendered  it  an  object  of  still  higher  am- 
bition. 

In  the  seventh  century  before  the  Christian  era,  as- 
tronomy began  to  be  cultivated  in  Greece ;  and  there 
arose  successively  three  celebrated  astronomical  schools, 
— the  school  of  Miletus,  the  school  of  Crotona,  and  the 
school  of  Alexandria.  The  first  was  established  by 
Thales,  six  hundred  and  forty  years  before  Christ ;  the 
second,  by  Pythagoras,  one  hundred  and  forty  years 
afterwards ;  and  the  third,  by  the  Ptolemies  of  Egypt, 
about  three  hundred  years  before  the  Christian  era 
As  Egypt  and  Babylon  were  renowned  among  the  most 
ancient  nations,  for  their  knowledge  of  the  sciences, 
long  before  they  were  cultivated  in  Greece,  it  was  the 
practice  of  the  Greeks,  when  they  aspired  to  the  char- 
acter of  philosophers  and  sages,  to  resort  to  these  coun- 
tries to  imbibe  wisdom  at  its  fountains.  Thales,  after 
extensive  travels  in  Crete  and  Egypt,  returned  to  his 
native  place,  Miletus,  a  town  on  the  coast  of  Asia  Minor, 
where  he  established  the  first  school  of  astronomy  in 
Greece.  Although  the  minds  of  these  ancient  astron- 
omers were  beclouded  with  much  error,  yet  Thales 
taught  a  few  truths  which  do  honor  to  his  sagacity. 
He  held  that  the  stars  are  formed  of  fire  ;  that  the 
moon  receives  her  light  from  the  sun,  and  is  invisible 
at  her  conjunctions  because  she  is  hid  in  the  sun's  rays. 
He  taught  the  sphericity  of  the  earth,  but  adopted  the 
common  error  of  placing  it  in  the  centre  of  the  world. 


SYSTEM  OF  THE  WORLD.  395 

He  introduced  the  division  of  the  sphere  into  five 
zones,  and  taught  the  obliquity  of  the  ecliptic.  He 
was  acquainted  with  the  Saros,  or  sacred  period  of  the 
Chaldeans,  (see  page  192,)  and  employed  it  in  calcu- 
lating eclipses.  It  was  Thales  that  predicted  the  fa- 
mous eclipse  of  the  sun  which  terminated  the  war  be- 
tween the  Lydians  and  the  Medes,  as  mentioned  in  a 
former  Letter.  Indeed,  Thales  is  universally  regarded 
as  a  bright  but  solitary  star,  glimmering  through  mists 
on  the  distant  horizon. 

To  Thales  succeeded,  in  the  school  of  Miletus,  two 
other  astronomers  of  much  celebrity,  Anaximander  and 
Anaxagoras.  Among  many  absurd  things  held  by  Anax- 
imander, he  first  taught  the  sublime  doctrine  that  the 
planets  are  inhabited,  and  that  the  stars  are  suns  of 
other  systems.  Anaxagoras  attempted  to  explain  all 
the  secrets  of  the  skies  by  natural  causes.  His  reason- 
ings, indeed,  were  alloyed  with  many  absurd  notions ; 
but  still  he  alone,  among  the  astronomers,  maintained 
the  existence  of  one  God.  His  doctrines  alarmed  his 
countrymen,  by  their  audacity  and  impiety  to  their 
gods,  whose  prerogatives  he  was  thought  to  invade  ; 
and,  to  deprecate  their  wrath,  sentence  of  death  was 
pronounced  on  the  philosopher  and  all  his  family, — a 
sentence  which  was  commuted  only  for  the  sad  alter- 
native of  perpetual  banishment.  The  very  genius  of 
the  heathen  mythology  was  at  war  with  the  truth. 
False  in  itself,  it  trained  the  mind  to  the  love  of  what 
was  false  in  the  interpretation  of  nature ;  it  arrayed 
itself  against  the  simplicity  of  truth,  and  persecuted  and 
put  to  death  its  most  ardent  votaries.  The  religion  of 
the  Bible,  on  the  other  hand,  lends  all  its  aid  to  truth 
in  nature  as  well  as  in  morals  and  religion.  In  its  very 
genius  it  inculcates  and  inspires  the  love  of  truth ;  it 
suggests,  by  its  analogies,  the  existence  of  established 
laws  in  the  system  of  the  world ;  and  holds  out  the 
moon  and  the  stars,  which  the  Creator  has  ordained, 
as  fit  objects  to  give  us  exalted  views  of  his  glory  and 
wisdom. 


396  LETTERS  ON  ASTRONOMY. 

Pythagoras  was  the  founder  of  the  celebrated  school 
of  Crotona.  He  was  a  native  of  Samos,  an  island  in 
the  JEgean  sea,  and  flourished  about  five  hundred  years 
before  the  Christian  era.  After  travelling  more  than 
thirty  years  in  Egypt  and  Chaldea,  and  spending  sev- 
eral years  more  at  Sparta,  to  learn  the  laws  and  institu- 
tions of  Lycurgus,  he  returned  to  his  native  island  to 
dispense  the  riches  he  had  acquired  to  his  countrymen. 
But  they,  probably  fearful  of  incurring  the  displeasure 
of  the  gods  by  the  freedom  with  which  he  inquired  into 
the  secrets  of  the  skies,  gave  him  so  unwelcome  a 
reception,  that  he  retired  from  them,  in  disgust,  and 
established  his  school  at  Crotona,  on  the  southeastern 
coast  of  Italy.  Hither,  as  to  an  oracle,  the  fame  of  his 
wisdom  attracted  hundreds  of  admiring  pupils,  whom 
he  instructed  in  every  species  of  knowledge.  From 
the  visionary  notions  which  are  generally  understood  to 
have  been  entertained  on  the  subject  of  astronomy,  by 
the  ancients,  we  are  apt  to  imagine  that  they  knew  less 
than  they  actually  did  of  the  truths  of  this  science. 
But  Pythagoras  was  acquainted  with  many  important 
facts  in  astronomy,  and  entertained  many  opinions  re- 
specting the  system  of  the  world,  which  are  now  held 
to  be  true.  Among  other  things  well  known  to  Py- 
thagoras, either  derived  from  his  own  investigations,  or 
received  from  his  predecessors,  were  the  following ;  and 
we  may  note  them  as  a  synopsis  of  the  state  of  astro- 
nomical knowledge  at  that  age  of  the  world.  First, 
the  principal  constellations.  These  had  begun  to  be 
formed  in  the  earliest  ages  of  the  world.  Several  of 
them,  bearing  the  same  name  as  at  present,  are  men- 
tioned in  the  writings  of  Hesiod  and  Homer ;  and  the 
"  sweet  influences  of  the  Pleiades,"  and  the  "  bands  of 
Orion,"  are  beautifully  alluded  to  in  the  book  of  Job. 
Secondly,  eclipses.  Pythagoras  knew  both  the  causes 
of  eclipses  and  how  to  predict  them ;  not,  indeed,  in 
the  accurate  manner  now  practised,  but  by  means  of 
the  Saros.  Thirdly,  Pythagoras  had  divined  the  true 
system  of  the  world,  holding  that  the  sun,  and  not  the 


SYSTEM  OP  TttE  WORLD.  397 

earth,  (as  was  generally  held  by  the  ancients,  even  for 
many  ages  after  Pythagoras,)  is  the  centre  around 
which  all  the  planets  revolve ;  and  that  the  stars  are  so 
many  suns,  each  the  centre  of  a  system  like  our  own. 
Among  lesser  things,  he  knew  that  the  earth  is  round ; 
that  its  surface  is  naturally  divided  into  five  zones  ;  and 
that  the  ecliptic  is  inclined  to  the  equator.  He  also 
held  that  the  earth  revolves  daily  on  its  axis,  and  year- 
ly around  the  sun  ;  that  the  galaxy  is  an  assemblage  of 
small  stars ;  and  that  it  is  the  same  luminary,  namely, 
Venus,  that  constitutes  both  the  morning  and  evening 
star ;  whereas  all  the  ancients  before  him  had  suppos- 
ed that  each  was  a  separate  planet,  and  accordingly 
the  morning  star  was  called  Lucifer,  and  the  evening 
star,  Hesperus.  He  held,  also,  that  the  planets  were 
inhabited,  and  even  went  so  far  as  to  calculate  the 
size  of  some  of  the  animals  in  the  moon.  Pythagoras 
was  also  so  great  an  enthusiast  in  music,  that  he  not 
only  assigned  to  it  a  conspicuous  place  in  his  system  of 
education,  but  even  supposed  that  the  heavenly  bodies 
themselves  were  arranged  at  distances  corresponding 
to  the  intervals  of  the  diatonic  scale,  and  imagined  them 
to  pursue  their  sublime  march  to  notes  created  by  their 
own  harmonious  movements,  called  the  '  music  of  the 
spheres ;'  but  he  maintained  that  this  celestial  concert,, 
though  loud  and  grand,  is  not  audible  to  the  feeble  or- 
gans of  man,  but  only  to  the  gods.  With  few  exceptions^ 
however,  the  opinions  of  Pythagoras  on  the  system  of  the 
world  were  founded  in  truth.  Yet  they  were  reject- 
ed by  Aristotle,  and  by  most  succeeding  astronomers, 
down  to  the  time  of  Copernicus ;  and  in  their  place 
was  substituted  the  doctrine  of  crystalline  spheres,  first 
taught  by  Eudoxus,  who  lived  about  three  hundred  and 
seventy  years  before  Christ.  According  to  this  system, 
the  heavenly  bodies  are  set  like  gems  in  hollow  solid 
orbs,  composed  of  crystal  so  transparent,  that  no  ante- 
rior orb  obstructs  in  the  least  the  view  of  any  of  the 
orbs  that  lie  behind  it.  The  sun  and  the  planets  have 
each  its  separate  orb ;  but  the  fixed  stars  are  all  set  in 
34  L.  A. 


398  LETTERS  ON  ASTRONOMY. 

the  same  grand  orb ;  and  beyond  this  is  another  still, 
the  primum  mobile,  which  revolves  daily,  from  east 
to  west,  and  carries  along  with  it  all  the  other  orbs. 
Above  the  whole  spreads  the  grand  empyrean,  or  third 
heavens,  the  abode  of  perpetual  serenity. 

To  account  for  the  planetary  motions,  it  was  sup- 
posed that  each  of  the  planetary  orbs,  as  well  as  that 
of  the  sun,  has  a  motion  of  its  own,  eastward,  while  it 
partakes  of  the  common  diurnal  motion  of  the  starry 
sphere.  Aristotle  taught  that  these  motions  are  effected 
by  a  tutelary  genius  of  each  planet,  residing  in  it,  and 
directing  its  motions,  as  the  mind  of  man  directs  his 
movements. 

Two  hundred  years  after  Pythagoras,  arose  the  fa- 
mous school  of  Alexandria,  under  the  Ptolemies.  These 
\vere  a  succession  of  Egyptian  kings,  and  are  not  to 
be  confounded  with  Ptolemy,  the  astronomer.  By  the 
munificent  patronage  of  this  enlightened  family,  for  the 
space  of  three  hundred  years,  beginning  at  the  death 
of  Alexander  the  Great,  from  whom  the  eldest  of  the 
Ptolemies  had  received  his  kingdom,  the  school  of  Al- 
exandria concentrated  in  its  vast  library  and  princely 
halls,  erected  for  the  accommodation  of  the  philoso- 
phers, nearly  all  the  science  and  learning  of  the  world. 
In  wandering  over  the  immense  territories  of  ignorance 
and  barbarism  which  covered,  at  that  time,  almost  the 
entire  face  of  the  earth,  the  eye  reposes  upon  this  little 
spot,  as  upon  a  verdant  island  in  the  midst  of  the  des- 
ert. Among  the  choice  fruits  that  grew  in  this  garden 
of  astronomy  were  several  of  the  most  distinguished 
ornaments  of  ancient  science,  of  whom  the  most  emi- 
nent were  Hipparchus  and  Ptolemy.  Hipparchus  is 
justly  considered  as  the  Newton  of  antiquity.  He 
sought  his  knowledge  of  the  heavenly  bodies  not  in  the 
illusory  suggestions  of  a  fervid  imagination,  but  in  the 
vigorous  application  of  an  intellect  of  the  first  order. 
Previous  to  this  period,  celestial  observations  were 
made  chiefly  with  the  naked  eye :  but  Hipparchus  was 
in  possession  of  instruments  for  measuring  angles,  and 


SYSTEM  OF  THE  WORLD.  399 

knew  how  to  resolve  spherical  triangles.  These  were 
great  steps  beyond  all  his  predecessors.  He  ascer- 
tained the  length  of  the  year  within  six  minutes  of  the 
truth.  He  discovered  the  eccentricity,  or  elliptical  fig- 
ure, of  the  solar  orbit,  although  he  supposed  the  sun 
actually  to  move  uniformly  in  a  circle,  but  the  earth  to 
be  placed  out  of  the  centre.  He  also  determined  the 
positions  of  the  points  among  the  stars  where  the  earth 
is  nearest  to  the  sun,  and  where  it  is  most  remote 
from  it.  He  formed  very  accurate  estimates  of  the  ob- 
liquity of  the  ecliptic  and  of  the  precession  of  the  equi- 
noxes. He  computed  the  exact  period  of  the  synodic 
revolution  of  the  moon,  and  the  inclination  of  the  lu- 
nar orbit ;  discovered  the  backward  motion  of  her  node 
and  of  her  line  of  apsides  ;  and  made  the  first  attempts 
to  ascertain  the  horizontal  parallaxes  of  the  sun  and 
moon.  Upon  the  appearance  of  a  new  star  in  the  fir- 
mament, he  undertook,  as  already  mentioned,  to  num- 
ber the  stars,  and  to  assign  to  each  its  true  place  in  the 
heavens,  in  order  that  posterity  might  have  the  means 
of  judging  what  changes,  if  any,  were  going  forward 
among  these  apparently  unalterable  bodies. 

Although  Hipparchus  is  generally  considered  as  be- 
longing to  the  Alexandrian  school,  yet  he  lived  at 
Rhodes,  and  there  made  his  astronomical  observations, 
about  one  hundred  and  forty  years  before  the  Christian 
era.  None  of  his  writings  have  come  down  to  us  ;  but 
his  principal  discoveries  have  been  transmitted  through 
the  '  Almagest'  of  Ptolemy.  Ptolemy  flourished  at  Al- 
exandria nearly  three  centuries  after  Hipparchus,  in 
the  second  century  after  Christ.  His  great  work,  the 
'  Almagest,'  which  has  conveyed  to  us  most  that  we 
know  respecting  the  astronomical  knowledge  of  the 
ancients,  was  the  universal  text-book  of  astronomers 
for  fourteen  centuries. 

The  name  of  this  celebrated  astronomer  has  also 
descended  to  us,  associated  with  the  system  of  the 
world  which  prevailed  from  Ptolemy  to  Copernicus, 
called  the  Ptolemaic  System.  The  doctrines  of  the 


400  LETTERS  ON  ASTRONOMY. 

Ptolemaic  system  did  not  originate  with  Ptolemy,  but, 
being  digested  by  him  out  of  materials  furnished  by 
various  hands,  it  has  come  down  to  us  under  the  sanc- 
tion of  his  name.  According  to  this  system,  the  earth 
is  the  centre  of  the  universe,  and  all  the  heavenly 
bodies  daily  revolve  around  it,  from  east  to  west.  But 
although  this  hypothesis  would  account  for  the  appar- 
ent diurnal  motion  of  the  firmament,  yet  it  would  not 
account  for  the  apparent  annual  motion  of  the  sun,  nor 
for  the  slow  motions  of  the  planets  from  west  to  east. 
In  order  to  explain  these  phenomena,  recourse  was  had 
to  deferents  and  epicycles, — an  explanation  devised  by 
Apollonius,  one  of  the  greatest  geometers  of  antiquity. 
He  conceived  that,  in  the  circumference  of  a  circle, 
having  the  earth  for  its  centre,  there  moves  the  centre 
of  a  smaller  circle  in  the  circumference  of  which  the 
planet  revolves.  The  circle  surrounding  the  earth 
was  called  the  deferent,  while  the  smaller  circle,  whose 
centre  was  always  in  the  circumference  of  the  deferent, 
was  called  the  epicycle.  Thus,  if  E,  Fig.  77,  represents 

the  earth,  ABC  will  be  the 
deferent,  and  D  F  G,  the  epicy- 
cle ;  and  it  is  obvious  that  the 
motion  of  a  body  from  west 
to  east,  in  this  small  circle, 
would  be  alternately  direct, 
stationary,  and  retrograde,  as 
was  explained,  in  a  previous 
Letter,  to  be  actually  the  case 
with  the  apparent  motions  of 
the  planets.  The  hypothesis, 
however,  is  inconsistent  with 
the  phases  of  Mercury  and 
Venus,  which,  being  between  us  and  the  sun,  on 
both  sides  of  the  epicycle,  would  present  their  dark 
sides  towards  us  at  both  conjunctions  with  the  sun, 
whereas,  at  one  of  the  conjunctions,  it  is  known 
that  they  exhibit  their  disks  illuminated.  It  is,  more- 
over, absurd  to  speak  of  a  geometrical  centre,  which 


SYSTEM  OF  THE  WORLD.  401 

has  no  bodily  existence,  moving  round  the  earth  on  the 
circumference  of  another  circle.  In  addition  to  these 
absurdities,  the  whole  Ptolemaic  system  is  encumbered 
with  the  following  difficulties :  First,  it  is  a  mere  hy- 
pothesis, having  no  evidence  in  its  favor  except  that  it 
explains  the  phenomena.  This  evidence  is  insufficient 
of  itself,  since  it  frequently  happens  that  each  of  two 
hypotheses,  which  are  directly  opposite  to  each  other, 
will  explain  all  the  known  phenomena.  But  the  Ptole- 
maic system  does  not  even  do  this,  as  it  is  inconsistent 
with  the  phases  of  Mercury  and  Venus,  as  already  ob- 
served. Secondly,  now  that  we  are  acquainted  with 
the  distances  of  the  remoter  planets,  and  especially  the 
fixed  stars,  the  swiftness  of  motion,  implied  in  a  daily 
revolution  of  the  starry  firmament  around  the  earth, 
renders  such  a  motion  wholly  incredible.  Thirdly,  the 
centrifugal  force  which  would  be  generated  in  these 
bodies,  especially  in  the  sun,  renders  it  impossible  that 
they  can  continue  to  revolve  around  the  earth  as  a  cen- 
tre. Absurd,  however,  as  the  system  of  Ptolemy  was, 
for  many  centuries  no  great  philosophic  genius  appeared 
to  expose  its  fallacies,  and  it  therefore  guided  the  faith 
of  astronomers  of  all  countries  down  to  the  time  of 
Copernicus. 

After  the  age  of  Ptolemy,  the  science  made  little 
progress.  With  the  decline  of  Grecian  liberty,  the 
arts  and  sciences  declined  also ;  and  the  Romans,  then 
masters  of  the  world,  were  ever  more  ambitious  to  gain 
conquests  over  man  than  over  matter ;  and  they  accord- 
ingly never  produced  a  single  great  astronomer.  Dur- 
ing the  middle  ages,  the  Arabians  were  almost  the  only 
astronomers,  and  they  cultivated  this  noble  study  chiefly 
as  subsidiary  to  astrology. 

At  length,  in  the  fifteenth  century,  Copernicus  arose, 
and  after  forty  years  of  intense  study  and  meditation, 
divined  the  true  system  of  the  world.  You  will  recol- 
lect that  the  Copernican  system  maintains,  1.  That  the 
apparent  diurnal  motions  of  the  heavenly  bodies,  from 
east  to  west,  is  owing  to  the  -real  revolution  of  the  earth 
34* 


402  LETTERS  ON  ASTRONOMY. 

on  its  own  axis  from  west  to  east ;  and,  2.  That  the 
sun  is  the  centre  around  which  the  earth  and  planets 
all  revolve  from  west  to  east.  It  rests  on  the  following 
arguments :  In  the  first  place,  the  earth  revolves  on  its 
own  axis.  First,  because  this  supposition  is  vastly  more 
simple.  Secondly,  it  is  agreeable  to  analogy,  since 
all  the  other  planets  that  afford  any  means  of  determin- 
ing the  question,  are  seen  to  revolve  on  their  axes. 
Thirdly,  the  spheroidal  figure  of  the  earth  is  the  fig- 
ure of  equilibrium,  that  results  from  a  revolution  on  its 
axis.  Fourthly,  the  diminished  weight  of  bodies  at 
the  equator  indicates  a  centrifugal  force  arising  from 
such  a  revolution.  Fifthly,  bodies  let  fall  from  a  high 
eminence,  fall  eastward  of  their  base,  indicating  that 
when  further  from  the  centre  of  the  earth  they  were 
subject  to  a  greater  velocity,  which,  in  consequence  of 
their  inertia,  they  do  not  entirely  lose  in  descending  to 
the  lower  level. 

In  the  second  place,  the  planets,  including  the  earth, 
revolve  about  the  sun.  First,  the  phases  of  Mercury 
and  Venus  are  precisely  such,  as  would  result  from 
their  circulating  around  the  sun  in  orbits  within  that 
of  the  earth ;  but  they  are  never  seen  in  opposition, 
as  they  would  be,  if  they  circulate  around  the  earth. 
Secondly,  the  superior  planets  do  indeed  revolve  around 
the  earth ;  but  they  also  revolve  around  the  sun,  as  is 
evident  from  their  phases,  and  from  the  known  dimen- 
sions of  their  orbits ;  and  that  the  sun,  and  not  the 
earth,  is  the  centre  of  their  motions,  is  inferred  from 
the  greater  symmetry  of  their  motions,  as  referred  to 
the  sun,  than  as  referred  to  the  earth ;  and  especially 
from  the  laws  of  gravitation,  which  forbid  our  suppos- 
ing that  bodies  so  much  larger  than  the  earth,  as  some 
of  these  bodies  are,  can  circulate  permanently  around 
the  earth,  the  latter  remaining  all  the  while  at  rest. 

In  the  third  place,  the  annual  motion  of  the  earth  it- 
self is  indicated  also  by  the  most  conclusive  arguments. 
For,  first,  since  all  the  planets,  with  their  satellites  and 
the  comets,  revolve  about  the  sun,  analogy  leads  us  to 


SYSTEM  OF  THE  WORLD.  403 

infer  the  same  respecting  the  earth  and  its  satellite,  as 
those  of  Jupiter  and  Saturn,  and  indicates  that  it  is  a  law 
of  the  solar  system  that  the  smaller  bodies  revolve  about 
the  larger.  Secondly,  on  the  supposition  that  the  earth 
performs  an  annual  revolution  around  the  sun,  it  is  em- 
braced along  with  the  planets,  in  Kepler's  law,  that  the 
squares  of  the  times  are  as  the  cubes  of  the  distances ; 
otherwise,  it  forms  an  exception,  and  the  only  known 
exception,  to  this  law. 

Such  are  the  leading  arguments  upon  which  rests  the 
Copernican  system  of  astronomy.  They  were,  howev- 
er, only  very  partially  known  to  Copernicus  himself,  as 
the  state  both  of  mechanical  science,  and  of  astronom 
ical  observation,  was  not  then  sufficiently  matured  to 
show  him  the  strength  of  his  own  doctrine,  since  he 
knew  nothing  of  the  telescope,  and  nothing  of  the  prin- 
ciple of  universal  gravitation.  The  evidence  of  this 
beautiful  system  being  left  by  Copernicus  in  so  imperfect 
a  state,  and  indeed  his  own  reasonings  in  support  of  it 
being  tinctured  with  some  errors,  we  need  not  so  much 
wonder  that  Tycho  Brahe,  who  immediately  followed 
Copernicus,  did  not  give  it  his  assent,  but,  influenced 
by  certain  passages  of  Scripture,  he  still  maintained, 
with  Ptolemy,  that  the  earth  is  in  the  centre  of  the  uni- 
verse ;  and  he  accounted  for  the  diurnal  motions  in  the 
same  manner  as  Ptolemy  had  done,  namely,  by  an  ac- 
tual revolution  of  the  whole  host  of  heaven  around  the 
earth  every  twenty-four  hours.  But  he  rejected  the 
scheme  of  deferents  and  epicycles,  and  held  that  the 
moon  revolves  about  the  earth  as  the  centre  of  her  mo- 
tions ;  but  that  the  sun  and  not  the  earth  is  the  centre 
of  the  planetary  motions ;  and  that  the  sun,  accompa- 
nied by  the  planets,  moves  around  the  earth  once  a 
year,  somewhat  in  the  manner  in  which  we  now  con- 
ceive of  Jupiter  and  his  satellites  as  revolving  around 
the  sun.  This  system  is  liable  to  most  of  the  objections 
that  lie  against  the  Ptolemaic  system,  with  the  disad- 
vantage of  being  more  complex. 

Kepler  and  Galileo,  however,  as  appeared  in  the 


404  LETTERS  ON  ASTRONOMY. 

sketch  of  their  lives,  embraced  the  theory  of  Copernicus 
with  great  avidity,  and  all  their  labors  contributed  to 
swell  the  evidence  of  its  truth.  When  we  see  with 
what  immense  labor  and  difficulty  the  disciples  of  Ptol- 
emy sought  to  reconcile  every  new  phenomenon  of  the 
heavens  with  their  system,  and  then  see  how  easily  and 
naturally  all  the  successive  discoveries  of  Galileo  and 
Kepler  fall  in  with  the  theory  of  Copernicus,  we  feel 
the  full  force  of  those  beautiful  lines  of  Cowper  which 
I  have  chosen  for  the  motto  of  this  Letter. 

Newton  received  the  torch  of  truth  from  Galileo,  and 
transmitted  it  to  his  successors,  with  its  light  enlarged 
and  purified ;  and  since  that  period,  every  new  discov- 
ery, whether  the  fruit  of  refined  instrumental  observa- 
tion or  of  profound  mathematical  analysis,  has  only 
added  lustre  to  the  glory  of  Copernicus. 

With  Newton  commenced  a  new  and  wonderful  era 
in  astronomy,  distinguished  above  all  others,  not  merely 
for  the  production  of  the  greatest  of  men,  but  also  for 
the  establishment  of  those  most  important  auxiliaries  to 
our  science,  the  Royal  Society  of  London,  the  Academy 
of  Sciences  at  Paris,  and  the  Observatory  of  Greenwich. 
I  may  add  the  commencement  of  the  Transactions  of 
the  Royal  Society,  and  the  Memoirs  of  the  Academy  of 
Sciences,  which  have  been  continued  to  the  present 
time, — both  precious  storehouses  of  astronomical  riches. 
The  Observatory  of  Greenwich,  moreover,  has  been  un- 
der the  direction  of  an  extraordinary  succession  of  great 
astronomers.  Their  names  are  Flamstead,  Halley,  Brad- 
ley, Maskeleyne,  Pond,  and  Airy, — the  last  being  still 
at  his  post,  and  worthy  of  continuing  a  line  so  truly  il- 
lustrious. The  observations  accumulated  at  this  cele- 
brated Observatory  are  so  numerous,  and  so  much  supe- 
rior to  those  of  any  other  institution  in  the  world,  that 
it  has  been  said  that  astronomy  would  suffer  little,  if  all 
other  contemporary  observations  of  the  same  kind  were 
annihilated.  Sir  William  Herschel,  however,  labored 
chiefly  in  a  different  sphere.  The  Astronomers  Royal 
devoted  themselves  not  so  much  to  the  discovery  of 


SYSTEM  OF  THE  WORLD.  405 

new  objects  among  the  heavenly  bodies,  as  to  the  exact 
determination  of  the  places  of  the  bodies  already  known, 
and  to  the  developement  of  new  laws  or  facts  among 
the  celestial  motions.  But  Herschel,  having  construct- 
ed telescopes  of  far  greater  reach  than  any  ever  used 
before,  employed  them  to  sound  new  and  untried  depths 
in  the  profundities  of  space.  We  have  already  seen 
what  interesting  and  amazing  discoveries  he  made  of 
double  stars,  clusters,  and  nebulae. 

The  English  have  done  most  for  astronomy  in  obser- 
vation and  discovery  ;  but  the  French  and  Germans,  in 
developing,  by  the  most  profound  mathematical  investi- 
gation, the  great  laws  of  physical  astronomy. 

It  only  remains  to  inquire,  whether  the  Copernican 
system  is  now  to  be  regarded  as  a  full  exposition  of  the 
'  Mechanism  of  the  Heavens/  or  whether  there  subsist 
higher  orders  of  relations  between  the  fixed  stars  them- 
selves. 

The  revolutions  of  the  binary  stars  afford  conclusive 
evidence  of  at  least  subordinate  systems  of  suns,  gov- 
erned by  the  same  laws  as  those  which  regulate  the 
motions  of  the  solar  system.  The  nebulce  also  compose 
peculiar  systems,  in  which  the  members  are  evidently 
bound  together  by  some  common  relation. 

In  these  marks  of  organization, — of  stars  associated 
together  in  clusters  ;  of  sun  revolving  around  sun  ;  and 
of  nebulae  disposed  in  regular  figures, — we  recognise 
different  members  of  some  grand  system,  links  in  one 
great  chain  that  binds  together  all  parts  of  the  universe ; 
as  we  see  Jupiter  and  his  satellites  combined  in  one 
subordinate  system,  and  Saturn  and  his  satellites  in  an- 
other,— each  a  vast  kingdom,  and  both  uniting  with  a 
number  of  other  individual  parts,  to  compose  an  empire 
still  more  vast. 

This  fact  being  now  established,  that  the  stars  are 
immense  bodies,  like  the  sun,  and  that  they  are  subject 
to  the  laws  of  gravitation,  we  cannot  conceive  how  they 
can  be  preserved  from  falling  into  final  disorder  and 
ruin,  unless  they  move  in  harmonious  concert,  like  the 


406  LETTERS  ON  ASTRONOMY. 

members  of  the  solar  system.  Otherwise,  those  that 
are  situated  on  the  confines  of  creation,  being  retained 
by  no  forces  from  without,  while  they  are  subject  to  the 
attraction  of  all  the  bodies  within,  must  leave  their  sta- 
tions, and  move  inward  with  accelerated  velocity ;  and 
thus  all  the  bodies  in  the  universe  would  at  length  fall 
together  in  the  common  centre  of  gravity.  The  im- 
mense distance  at  which  the  stars  are  placed  from  each 
other  would  indeed  delay  such  a  catastrophe ;  but  this 
must  be  the  ultimate  tendency  of  the  material  world, 
unless  sustained  in  one  harmonious  system  by  nicely- 
adjusted  motions.  To  leave  entirely  out  of  view  our 
confidence  in  the  wisdom  and  preserving  goodness  of 
the  Creator,  and  reasoning  merely  from  what  we  know 
of  the  stability  of  the  solar  system,  we  should  be  justi- 
fied in  inferring,  that  other  worlds  are  not  subject  to 
forces  which  operate  only  to  hasten  their  decay,  and  to 
involve  them  in  final  ruin. 

We  conclude,  therefore,  that  the  material  universe 
is  one  great  system ;  that  the  combination  of  planets 
with  their  satellites  constitutes  the  first  or  lowest  order 
of  worlds ;  that  next  to  these,  planets  are  linked  to 
suns ;  that  these  are  bound  to  other  suns,  composing 
a  still  higher  order  in  the  scale  of  being ;  and  finally, 
that  all  the  different  systems  of  worlds  move  around 
their  common  centre  of  gravity. 


LETTER  XXXI. 


CONCLUSION. 


Philosophy,  baptized 


--  , 

In  the  pure  fountain  of  Eternal  Love, 
Has  eyes  indeed  ;  and,  viewing  all  she  sees 
As  meant  to  indicate  a  God  to  man, 
Gives  Him  the  praise,  and  forfeits  not  her  own."  —  Cowper. 

I  INTENDED,  my  dear  Friend,  to  comply  with  your 
request  "  that  I  would  discuss  the  arguments  which  as- 


CONCLUSION.  401 

tronomy  affords  to  natural  theology  ;"  but  these  Letters 
have  been  already  extended  so  much  further  than  I  an- 
ticipated, that  I  shall  conclude  with  suggesting  a  few 
of  those  moral  and  religious  reflections,  which  ought  al- 
ways to  follow  in  the  train  of  such  a  survey  of  the  heav- 
enly bodies  as  we  have  now  taken. 

Although  there  is  evidence  enough  in  the  structure, 
arrangement,  and  laws,  which  prevail  among  the  heav- 
enly bodies,  to  prove  the  existence  of  God,  yet  I  think 
there  are  many  subordinate  parts  of  His  works  far  bet- 
ter adapted  to  this  purpose  than  these,  being  more  fully 
within  our  comprehension.  It  was  intended,  no  doubt, 
that  the  evidence  of  His  being  should  be  accessible  to 
all  His  creatures,  and  should  not  depend  on  a  kind  of 
knowledge  possessed  by  comparatively  few.  The  mech- 
anism of  the  eye  is  probably  not  more  perfect  than 
that  of  the  universe  ;  but  we  can  analyze  it  better,  and 
more  fully  understand  the  design  of  each  part.  But  the 
existence  of  God  being  once  proved,  and  it  being 
admitted  that  He  is  the  Creator  and  Governor  of  the 
world,  then  the  discoveries  of  astronomy  are  admirably 
adapted  to  perform  just  that  office  in  relation  to  the 
Great  First  Cause,  which  is  assigned  to  them  in  the  Bi- 
ble, namely, "  to  declare  the  glory  of  God,  and  to  show 
His  handiwork."  In  other  words,  the  discoveries  of 
astronomy  are  peculiarly  fitted, — more  so,  perhaps,  than 
any  other  department  of  creation, — to  exhibit  the  uni- 
ty, power,  and  wisdom,  of  the  Creator. 

The  most  modern  discoveries  have  multiplied  the 
proofs  of  the  unity  of  God.  It  has  usually  been  offer- 
ed as  sufficient  evidence  of  the  truth  of  this  doctrine, 
that  the  laws  of  Nature  are  found  to  be  uniform  when 
applied  to  the  utmost  bounds  of  the  solar  system ;  that 
the  law  of  gravitation  controls  alike  the  motions  of  Mer- 
cury, and  those  of  Uranus ;  and  that  its  operation  is  one 
and  the  same  upon  the  moon  and  upon  the  satellites 
of  Saturn.  It  was,  however,  impossible,  until  recently, 
to  predicate  the  same  uniformity  in  the  great  laws  of 
the  universe  respecting  the.  starry  worlds,  except  by  a 


408  LETTERS  ON  ASTRONOMY. 

feeble  analogy.  However  improbable,  it  was  still  possi- 
ble, that  in  these  distant  worlds  other  laws  might  pre- 
vail, and  other  Lords  exercise  dominion.  But  the  dis- 
covery of  the  revolutions  of  the  binary  stars,  in  exact 
accordance  with  the  law  of  gravitation,  not  merely  in 
a  single  instance,  but  in  many  instances,  in  all  cases, 
indeed,  wherever  those  revolutions  have  advanced  so 
far  as  to  determine  their  law  of  action,  gives  us  demon- 
stration, instead  of  analogy,  of  the  prevalence  of  the 
same  law  among  the  other  systems  as  that  which  rules 
in  ours. 

The  marks  of  a  still  higher  organization  in  the  struc- 
ture of  clusters  and  nebulae,  all  bearing  that  same  char- 
acteristic union  of  resemblance  and  variety  which  be- 
longs to  all  the  other  works  of  creation  that  fall  under 
our  notice,  speak  loudly  of  one,  and  only  one,  grand  de- 
sign. Every  new  discovery  of  the  telescope,  therefore, 
has  added  new  proofs  to  the  great  truth  that  God  is 
one :  nor,  so  far  as  I  know,  has  a  single  fact  appeared, 
that  is  not  entirely  consonant  with  it.  Light,  more- 
over, which  brings  us  intelligence,  and,  in  most  cases, 
the  only  intelligence  we  have,  of  these  remote  orbs,  tes- 
tifies to  the  same  truth,  being  similar  in  its  properties 
and  uniform  in  its  motions,  from  whatever  star  it  em- 
anates. 

In  displays  of  the  power  of  Jehovah,  nothing  can 
compare  with  the  starry  heavens.  The  magnitudes, 
distances,  and  velocities,  of  the  heavenly  bodies  are  so 
much  beyond  every  thing  of  this  kind  which  belongs 
to  things  around  us,  from  which  we  borrowed  our  first 
ideas  of  these  qualities,  that  we  can  scarcely  avoid  look- 
ing with  incredulity  at  the  numerical  results  to  which 
the  unerring  principles  of  mathematics  have  conducted 
us.  And  when  we  attempt  to  apply  our  measures  to 
the  fixed  stars,  and  especially  to  the  nebulae,  the  result 
is  absolutely  overwhelming :  the  mind  refuses  its  aid  in 
our  attempts  to  grasp  the  great  ideas.  Nor  less  conspic- 
uous, among  the  phenomena  of  the  heavenly  bodies,  is 
the  wisdom  of  the  Creator.  In  the  first  place,  this  at- 


CONCLUSION.  409 

tribute  is  every  where  exhibited  in  the  happy  adap- 
tation of  means  to  their  ends.  No  principle  can  be 
imagined  more  simple,  and  at  the  same  time  more  ef- 
fectual to  answer  the  purposes  which  it  serves,  than 
gravitation.  No  position  can  be  given  to  the  sun  and 
planets  so  fitted,  as  far  as  we  can  judge,  to  fulfil  their 
mutual  relations,  as  that  which  the  Creator  has  given 
them.  I  say,  as  far  as  we  can  judge  ;  for  we  find  this 
to  be  the  case  in  respect  to  our  own  planet  and  its  at- 
tendant satellite,  and  hence  have  reason  to  infer  that 
the  same  is  the  case  in  the  other  planets,  evidently 
holding,  as  they  do,  a  similar  relation  to  the  sun.  Thus 
the  position  of  the  earth  at  just  such  a  distance  from 
the  sun  as  suits  the  nature  of  its  animal  and  vegetable 
kingdoms,  and  confining  the  range  of  solar  heat,  vast 
as  it  might  easily  become,  within  such  narrow  bounds  ; 
the  inclination  of  the  earth's  axis  to  the  plane  of  its 
orbit,  so  as  to  produce  the  agreeable  vicissitudes  of  the 
seasons,  and  increase  the  varieties  of  animal  and  veg- 
etable life,  still  confining  the  degree  of  inclination  so 
exactly  within  the  bounds  of  safety,  that,  were  it  much 
to  transcend  its  present  limits,  the  changes  of  tempera- 
ture of  the  different  seasons  would  be  too  sudden  and 
violent  for  the  existence  of  either  animals  or  vegetables  ; 
the  revolution  of  the  earth  on  its  axis,  so  happily  di- 
viding time  into  hours  of  business  and  of  repose ;  the 
adaptation  of  the  moon  to  the  earth,  so  as  to  afford  to 
us  her  greatest  amount  of  light  just  at  the  times  when- 
it  is  needed  most,  and  giving  to  the  moon  just  such  a 
quantity  of  matter,  and  placing  her  at  just  such  a  dis- 
tance from  the  earth,  as  serves  to  raise  a  tide  produc- 
tive of  every  conceivable  advantage,  without  the  evils 
which  would  result  from  a  stagnation  of  the  waters  on 
the  one  hand,  or  from  their  overflow  on  the  other ; — 
these  are  a  few  examples  of  the  wisdom  displayed  in 
the  mutual  relations  instituted  between  the  sun,  the 
earth,  and  the  moon. 

In  the  second  place,  similar  marks  of  wisdom  are  ex- 
hibited in  the  many  useful  and  important  purposes 
35  L.  A. 


410  LETTERS  ON  ASTRONOMY. 

which  the  same  thing  is  mode  to  serve.  Thus  the  sun 
is  at  once  the  great  regulator  of  the  planetary  motions, 
and  the  fountain  of  light  and  heat.  The  moon  both 
gives  light  by  night  and  raises  the  tides.  Or,  if  we 
would  follow  out  this  principle  where  its  operations  are 
more  within  our  comprehension,  we  may  instance  the 
atmosphere.  When  man  constructs  an  instrument,  he 
deems  it  sufficient  if  it  fulfils  one  single  purpose  ;  as  the 
watch,  to  tell  the  hour  of  the  day,  or  the  telescope,  to 
enable  him  to  see  distant  objects ;  and  had  a  being  like 
ourselves  made  the  atmosphere,  he  would  have  thought 
it  enough  to  have  created  a  medium  so  essential  to 
animal  life,  that  to  live  is  to  breathe,  and  to  cease  to 
breathe  is  to  die.  But  beside  this,  the  atmosphere  has 
manifold  uses,  each  entirely  distinct  from  all  the  others. 
It  conveys  to  plants,  as  well  as  animals,  their  nourish- 
ment and  life  ;  it  tempers  the  heat  of  Summer  with  its 
breezes;  it  binds  down  all  fluids,  and  prevents  their 
passing  into  the  state  of  vapor ;  it  supports  the  clouds, 
distils  the  dew,  and  waters  the  earth  with  showers ;  it 
multiplies  the  light  of  the  sun,  and  diffuses  it  over  earth 
and  sky ;  it  feeds  our  fires,  turns  our  machines,  wafts 
our  ships,  and  conveys  to  the  ear  all  the  sentiments  of 
language,  and  all  the  melodies  of  music. 

In  the  third  place,  the  wisdom  of  the  Creator  is  strik- 
ingly manifested  in  the  provision  he  has  made  for  the 
stability  of  the  universe.  The  perturbations  occasioned 
by  the  motions  of  the  planets,  from  their  action  on  each 
other,  are  very  numerous,  since  every  body  in  the  sys- 
tem exerts  an  attraction  on  every  other,  in  conformity 
with  the  law  of  universal  gravitation.  Venus  and  Mer- 
cury, approaching,  as  they  do  at  times,  comparatively 
near  to  the  earth,  sensibly  disturb  its  motions ;  and  the 
satellites  of  the  remoter  planets  greatly  disturb  each 
other's  movements.  Nor  was  it  possible  to  endow  this 
principle  with  the  properties  it  has,  and  make  it  operate 
as  it  does  in  regulating  the  motions  of  the  world,  with- 
out involving  such  an  incident.  On  this  subject,  Pro- 
fessor Whewell,  in  his  excellent  work  composing  one  of 


CONCLUSION.  411 

the  Bridgewater  Treatises,  remarks :  "  The  derangement 
which  the  planets  produce  in  the  motion  of  one  of  their 
number  will  be  very  small,  in  the  course  of  one  revolu- 
tion ;  but  this  gives  us  no  security  that  the  derangement 
may  not  become  very  large,  in  the  course  of  many  rev- 
olutions. The  cause  acts  perpetually,  and  it  has  the 
whole  extent  of  time  to  work  in.  Is  it  not  easily  con- 
ceivable, then,  that,  in  the  lapse  of  ages,  the  derange- 
ments of  the  motions  of  the  planets  may  accumulate, 
the  orbits  may  change  their  form,  and  their  mutual  dis- 
tances may  be  much  increased  or  diminished  ?  Is  it 
not  possible  that  these  changes  may  go  on  without  limit, 
and  end  in  the  complete  subversion  and  ruin  of  the 
system  ?  If,  for  instance,  the  result  of  this  mutual  grav- 
itation should  be  to  increase  considerably  the  eccen- 
tricity of  the  earth's  orbit,  or  to  make  the  moon  approach 
continually  nearer  and  nearer  to  the  earth,  at  every 
revolution,  it  is  easy  to  see  that,  in  the  one  case,  our 
year  would  change  its  character,  producing  a  far  greater 
irregularity  in  the  distribution  of  the  solar  heat ;  in  the 
other,  our  satellite  must  fall  to  the  earth,  occasioning  a 
dreadful  catastrophe.  If  the  positions  of  the  planetary 
orbits,  with  respect  to  that  of  the  earth,  were  to  change 
much,  the  planets  might  sometimes  come  very  near  us, 
and  thus  increase  the  effect  of  their  attraction  beyond 
calculable  limits.  Under  such  circumstances, c  we  might 
have  years  of  unequal  length,  and  seasons  of  capricious 
temperature  ;  planets  and  moons,  of  portentous  size  and 
aspect,  glaring  and  disappearing  at  uncertain  intervals ; 
tides,  like  deluges,  sweeping  over  whole  continents; 
and  perhaps  the  collision  of  two  of  the  planets,  and  the 
consequent  destruction  of  all  organization  on  both  of 
them.'  The  fact  really  is,  that  changes  are  taking  place 
in  the  motions  of  the  heavenly  bodies,  which  have  gone 
on  progressively,  from  the  first  dawn  of  science.  The 
eccentricity  of  the  earth's  orbit  has  been  diminishing 
from  the  earliest  observations  to  our  times.  The  moon 
has  been  moving  quicker  from  the  time  of  the  first  re- 
corded eclipses,  and  is  now-  in  advance,  by  about  four 


412  LETTERS  ON  ASTRONOMY. 

times  her  own  breadth,  of  what  her  own  place  would 
have  been,  if  it  had  not  been  affected  by  this  accelera- 
tion. The  obliquity  of  the  ecliptic,  also,  is  in  a  state 
of  diminution,  and  is  now  about  two  fifths  of  a  degree 
less  than  it  was  in  the  time  of  Aristotle." 

But  amid  so  many  seeming  causes  of  irregularity  and 
ruin,  it  is  worthy  of  a  grateful  notice,  that  effectual  pro- 
vision is  made  for  the  stability  of  the  solar  system.  The 
full  confirmation  of  this  fact  is  among  the  grand  results 
of  physical  astronomy.  "  Newton  did  not  undertake  to 
demonstrate  either  the  stability  or  instability  of  the  sys- 
tem. The  decision  of  this  point  required  a  great  num- 
ber of  preparatory  steps  and  simplifications,  and  such 
progress  in  the  invention  and  improvement  of  mathe- 
matical methods,  as  occupied  the  best  mathematicians 
of  Europe  for  the  greater  part  of  the  last  century.  Tow- 
ards the  end  of  that  time,  it  was  shown  by  La  Grange 
and  La  Place,  that  the  arrangements  of  the  solar  sys- 
tem are  stable ;  that,  in  the  long  run,  the  orbits  and 
motions  remain  unchanged ;  and  that  the  changes  in 
the  orbits,  which  take  place  in  shorter  periods,  never 
transgress  certain  very  moderate  limits.  Each  orbit 
undergoes  deviations  on  this  side  and  on  that  side  of 
its  average  state ;  but  these  deviations  are  never  very 
great,  and  it  finally  recovers  from  them,  so  that  the 
average  is  preserved.  The  planets  produce  perpetual 
perturbations  in  each  other's  motions ;  but  these  per- 
turbations are  not  indefinitely  progressive,  but  periodi- 
cal, reaching  a  maximum  value,  and  then  diminishing. 
The  periods  which  this  restoration  requires  are,  for  the 
most  part,  enormous, — not  less  than  thousands,  and  in 
some  instances,  millions,  of  years.  Indeed,  some  of 
these  apparent  derangements  have  been  going  on  in  the 
same  direction  from  the  creation  of  the  world.  But  the 
restoration  is  in  the  sequel  as  complete  as  the  derange- 
ment ;  and  in  the  mean  time  the  disturbance  never  at- 
tains a  sufficient  amount  seriously  to  affect  the  stability 
of  the  system.  '  I  have  succeeded  in  demonstrating/ 
says  La  Place,  *  that,  whatever  be  the  masses  of  the 


CONCLUSION.  413 

planets,  in  consequence  of  the  fact  that  they  all  move 
in  the  same  direction,  in  orbits  of  small  eccentricity, 
and  but  slightly  inclined  to  each  other,  their  secular  ir- 
regularities are  periodical,  and  included  within  narrow 
limits ;  so  that  the  planetary  system  will  only  oscillate 
about  a  mean  state,  and  will  never  deviate  from  it,  ex- 
cept by  a  very  small  quantity.  The  ellipses  of  the 
planets  have  been  and  always  will  be  nearly  circular. 
The  ecliptic  will  never  coincide  with  the  equator ;  and 
the  entire  extent  of  the  variation,  in  its  inclination,  can- 
not exceed  three  degrees.' ': 

To  these  observations  of  La  Place,  Professor  Whewell 
adds  the  following,  on  the  importance,  to  the  stability 
of  the  solar  system,  of  the  fact  that  those  planets  which 
have  great  masses  have  orbits  of  small  eccentricity. 
"The  planets  Mercury  and  Mars,  which  have  much 
the  largest  eccentricity  among  the  old  planets,  are 
those  of  which  the  masses  are  much  the  smallest.  The 
mass  of  Jupiter  is  more  than  two  thousand  times  that 
of  either  of  these  planets.  If  the  orbit  of  Jupiter  were 
as  eccentric  as  that  of  Mercury,  all  the  security  for 
the  stability  of  the  system,  which  analysis  has  yet 
pointed  out,  would  disappear.  The  earth  and  the 
smaller  planets  might,  by  the  near  approach  of  Jupiter 
at  his  perihelion,  change  their  nearly  circular  orbits 
into  very  long  ellipses,  and  thus  might  fall  into  the  sun, 
or  fly  off  into  remoter  space.  It  is  further  remarkable, 
that  in  the  newly-discovered  planets,  of  which  the  or- 
bits are  still  more  eccentric  than  that  of  Mercury,  the 
masses  are  still  smaller,  so  that  the  same  provision  is 
established  in  this  case,  also." 

With  this  hasty  glance  at  the  unity,  power,  and  wis- 
dom, of  the  Creator,  as  manifested  in  the  greatest  of 
His  works,  I  close.  I  hope  enough  has  been  said  to 
vindicate  the  sentiment  that  called  '  Devotion,  daughter 
of  Astronomy !'  I  do  not  pretend  that  this,  or  any 
other  science,  is  adequate  of  itself  to  purify  the  heart,  or 
to  raise  it  to  its  Maker ;  but  I  fully  believe  that,  when 
the  heart  is  already  under  the  power  of  religion,  there 
35* 


414  LETTERS  ON  ASTRONOMY. 

is  something  in  the  frequent  and  habitual  contemplation 
of  the  heavenly  bodies  under  all  the  lights  of  modern 
astronomy,  very  favorable  to  devotional  feelings,  in- 
spiring, as  it  does,  humility,  in  unison  with  an  exalted 
sentiment  of  grateful  adoration. 

I  have  thus,  my  dear  Friend,  responded  to  your  call, 
in  such  a  manner  as  I  could,  in  the  transient  intervals 
between  severer  professional  studies,  and  by  appropri- 
ating to  you  nearly  the  whole  of  my  long  vacation.  In 
giving  publicity  to  these  Letters,  how  happy  should  I 
be,  to  find  that  they  prove  acceptable  and  even  attrac- 
tive to  the  youth  of  our  country,  of  both  sexes.  The 
inquiry  has  often  pressed  itself  upon  me,  when  enjoy- 
ing myself  so  high  a  degree  of  pleasure  from  the  stu- 
dy of  both  the  science  and  the  literature  of  astrono- 
my,— Cannot  the  reading  community,  especially  the 
youthful  part  of  it,  learn  how  much  more  solid  and 
enduring  pleasure  is  to  be  derived  from  truth  than  from 
fiction  ?  Sated  as  the  present  age  has  been  with  ficti- 
tious narratives,  is  it  not  ready  for  a  change  ?  And 
if  truth  can  be  disrobed  of  her  severity,  and  arrayed  in 
a  more  attractive  garb  than  she  usually  wears,  is  not 
this  a  favorable  moment  for  bringing  her  forward  from 
the  obscurity  into  which  she  has  long  been  forced  by 
her  powerful  rival  ?  In  the  schools,  indeed,  where  men- 
tal discipline  is  the  leading  object,  science  must  be  per- 
mitted to  retain  her  wonted  rigor ;  but  I  see  not  why, 
for  the  purposes  of  the  general  reader,  she  may  not  re- 
lax her  features,  and  be  happily  allied  with  her  own  lit- 
erature. That  you,  dear  Madam,  will  use  your  influence 
to  effect  such  a  change  of  taste  among  your  youthful 
friends,  as  may  lead  them  to  prefer  the  interesting  and 
exalted  truths  of  astronomy  above  the  most  enticing 
works  of  fiction,  I  cannot  for  a  moment  doubt.  And 
in  this  expectation,  I  bid  you,  affectionately, 

ADIEU. 


INDEX. 


A. 

Bellatrix,   .     ;  V        . 

375 

Alamak,     . 

.    371 

Betalgeus,  '    *     ;  ,. 

375 

Aldebaran,     . 

369 

Bissextile,           .         .         . 

64 

Alexandrian  school,    . 

.    394 

Bootes,        .  "  .'        ;' 

372 

Algenib,        <A      "  •    - 

371 

Bouguer,    .         .         .-,,»•" 

74 

Algol,         .  ':.,.> 

.    371 

Bowditch,       .        ,  •  :  ,.;^  .-,, 

148 

Alioth,  .         .         fa 

374 

Brahean  system, 

403 

Almagest,  .   ,.     »        .« 

.       14 

Altair,  .     •PV\'Y1" 

373 

C. 

Altitude,    .         .'.     .   .' 

.      20 

Caesar,  Julius,    .         .     ,  :. 

64 

Amplitude,    .         »  s; 

;        20 

Calendar,  Grecian,         .  ,  -r 

67 

Anaxagoras,        .    .     w( 

.    395 

**          Gregorian,       ,   «' 

65 

Anaximander,         * 

395 

Cancer,           .      ,  .        . 

369 

Andromeda, 

.    371 

Canis  Major, 

375 

Antares, 

370 

Canis  Minor,           ..( 

375 

Antinous,   . 

.    373 

Capella,     . 

372 

Apogee, 

187 

Capricorn,    .        .„•/,«.., 

370 

Apsides,     . 

.     188 

Cassiopeia,          .         .     •.   »; 

374 

Aquarius, 

371 

Catalogues  of  the  stars,  . 

367 

373 

Central  forces,    . 

130 

Archimedes,  .        -v 

136 

Cepheus,        w^  f-  • 

374 

A  returns,   .       V  :  '  ^ 

.    372 

Ceres,         .       ,*':v,.-><*  -i  >5. 

287 

Aries,    . 

,*',     369 

Cetus,    .... 

374 

Aristotle,   . 

.    136 

Chronology, 

157 

Astrology,       .    v  . 

393 

Chronometers, 

210 

Astronomers  royal, 

48,  404 

Circles,  great  and  small,     . 

19 

Astronomical  clock, 

51 

**       of  diurnal  revolution 

,    81 

Astronomical  tables,  . 

.     190 

"       of  perpetual  appa- 

Astronomy,   .        •. 

'...""       17 

rition, 

85 

"           history  of, 

14,392 

**       of  perpetual  occul- 

Atmosphere, 

100,  410 

tation, 

85 

Attraction, 

135 

"       vertical,     . 

20 

371 

Clusters,                      . 

376 

Axis  of  the  Earth,  . 

-w           21 

Colures,         •.*        . 

23 

Azimuth,    .         .       •«*£ 

.      20 

Coma  Berenices,         .  ,       . 

372 

Comet,  Biela's,       .       ,  . 

339 

B. 

"      Encke's, 

840 

Bacon, 

16,  136 

'«      Halley's,    .     ;{  ^ 

323 

Base  line, 

76 

Comets,     .... 

313 

Base  of  verification,   . 

.      79 

«'       brightness  of,    . 

315 

416 


INDEX. 


Comets,  distances  of,  . 

317 

Equations,  periodical, 

193 

light  of,     . 

317 

"            secular, 

193 

magnitude  of, 

315 

"           tabular,     . 

190 

mass  of,    . 

318 

Equator, 

21 

motions  of,    . 

320 

Equinoxes, 

22 

number  of, 

315 

*'           precession  of  the, 

154 

periods  of,     . 

316 

Eudoxus,    .... 

397 

perturbations  of, 

319 

structure  of,  . 

314 

F. 

tails  of,     . 

317 

Fomalhaut, 

371 

Complement, 

18 

Fraunhofer,    . 

37 

Conjunction,  . 

200 

Constellations,    . 

366 

G. 

Copernican  system,          256, 

401 

Galaxy,      .... 

379 

Copernicus,         .         .       14, 

255 

Galileo, 

15 

Cor  Caroli, 

372 

"       abjuration  of, 

272 

Cor  Hydrae, 

375 

"       condemnation  of, 

266 

Corona  Borealis,     . 

372 

"       life  of,  . 

258 

Corvus,      .... 

375 

**       persecutions  of, 

265 

Crotona, 

394 

Gemini,      .... 

369 

Crystalline  spheres,    . 

397 

Gemma, 

372 

Cygnus,          .  .      •  ...    . 

374 

Globes,  artificial, 

25 

* 

Gravitation,  universal,    . 

145 

D. 

Gravity,  terrestrial,     . 

134 

Day,  astronomical, 

61 

"     sidereal,     . 

60 

H. 

....  60 

Days  of  the  week,      .  .      68 

Declination,    ...  24 

Deferents,           .         .  .    400 

Denebola,       .          .          .  370 
Distances    of   the    heavenly 

bodies,  how  measured,  .      94 

Distances  of  the  stars,     .  387 

Dolphin,     .         .         .  .373 

Double  stars,           .         .  381 

Draco,        .         .         .  .374 


E. 

Earth,  diameter  of  the, 
"      ellipticity  of  the, 
"      figure  of  the,    . 
"      motion  of  the, 
"      orbit  of  the,     . 

Eclipses,  annular, 
"  calculation  of, 

'*          of  the  moon,    . 
"  of  the  sun,    . 

Ecliptic, 

Epicycles, 

Equation  of  time,  . 


Hercules,  ....  372 

Herschel,  Sir  Wm.,  36,  105,  383 

Hesperus,            .         .          .  397 

Hipparchus,   .         .         .  398 

Horizon,  rational,        .          .  20 

"         sensible,  .         .  20 

Hour-circles,       ...  21 

Huyghens,      ...  72 

I. 

Inductive  system,        .         .  137 

Inquisition,     .          .          .  138 

Instruments,  astronomical,  29 


78 

78 

J. 

69 

Juno, 

. 

288 

126 

Jupiter, 

. 

247 

149 

« 

belts  of, 

248 

204 

« 

diameter  of, 

247 

201 

« 

distance  of,    . 

247 

195 

« 

eclipses  of, 

250 

203 

cc 

magnitude  of, 

247 

22 

(( 

satellites  of, 

250 

400 

ct 

scenery  of,    . 

247 

61 

(( 

telescopic  view  of, 

247 

INDEX. 


417 


K. 

Kepler,      .         .         .         .300 
Kepler's  law«,        .         .         296 


Latitude,   .... 
"        how  found, 

Laws  of  motion,         ,    ">  {* 
"        terrestrial  gravity, 

Leap  year, 

Leo,       .         .         .      .-*>jti« 

Leo  Minor, 

Libra,    .... 

Librations  of  the  moon, 

Light,    velocity    of,    how 
measured,     .         .  ,<& ... 

Longitude,  celestial,      '-r#:''. 
terrestrial, 
its  importance, 
how  found, 
by  chronometers, 
by  eclipses, 
by  Jupiter's  sat- 
ellites, .    -;  -y 


22 

210 
126 
139 
64 
370 
372 
370 
179 

252 
24 
22 

208 
210 
210 
212 

251 

"  by  lunar  method,  213 

Lucifer,      .         .         .         .397 
Lynx,     ....         372 

M. 

Magnitudes,  how  measured,  94 

Magellan  clouds,         .         .  378 

Mars,  245 

"     changes  of,         .         .  245 

«'     distance  of,  .         .  245 

"     revolutions  of,  .         .  246 

Mecanique  Celeste,         .  148 

Mercury,    ....  230 

**         conjunctions  of,  231 

"         diurnal  revolution  of,  235 

"         phases  of,  .         .  234 

"         sidereal  revolut'n  of,  231 

"         synodical       "  231 

"         transits  of,     .         .  237 

Meridian,        .      '•>'.'•-  £  •-'•  20 

Meteoric  showers,       .         .  346 

"             "       origin  of,  350 

Meteoric  stones,          .         .  290 

Metonic  cycle,         .         .  192 

Miletus,  school  of,      .         .  394 

Milky  Way,  ...  379 

Mira,          .         .   e     .         .  375 


Mirach,      .         .         .  .371 

Mizar,    .        •.„•'.  '.     .    «fe  374 

Month,  sidereal,      '•  .    -  .173 

"      synodical,  .         .  173 

Moon,         .         .         .  .157 

atmosphere  of  the,  167 

cusps  of  the,    .  .    174 

diameter  of  the,    .  158 

distance  of  the,  .    158 

eclipses  of  the,      .  195 

harvest,    .         .  .    177 

irregularities  of  the,  186 

librations  of  the,  .    179 

light  of  the,  .        .  158 

mountains  in  the,  .    159 

nodes  of  the,         .  173 

phases  of  the,  .  .    174 
revolutions  of  the,  178-182 

scenery  of  the,  .     163 
telescopic     appear- 

ance of  the,  .  .    158 

volcanoes  in  the,    .  166 

volume  of  the,  .    158 

Motion,  laws  of,     .         .  126 

Motions  of  the  planets,  .    291 

Mural  circle,        '  .-;-       J''-  54 

N. 

Nadir,         ....  20 

Nature  of  the  stars,         .  390 

Nebulte,     .         .         .  .377 

New  planets,          .         .  286 

"             distances  of,  ,    288 

"             origin  of,    .  289 

"             periods  of,  .    288 

"             size  of,        .  289 

New  style,          ...  66 


Newton, 


.  16,143 


O. 


Oblique  sphere,  .         .      84 

Obliquity  of  the  ecliptic,         115 

"       effect  of,  on  the 

Seasons,  .         .123 

"       how  found,      .         117 
Observatory,       ...      42 

"  Greenwich,     42-48 

"  Tycho's,         .      42 

Old  style,       .      ''-.>.'       66 
Ophiucus,  .       ,.         .    872 

Opposition,    .         .        .        200 


418 


INDEX. 


Orion,    .... 

375 

Regulus,    .... 

370 

Orreries,    .         .         .     112, 

292 

Resolution  of  motion, 

132 

Resultant, 

132 

P. 

Revolution,  annual, 

111 

Pallas,        .... 

287 

diurnal,    . 

111 

Parallactic  arc, 

91 

Rigel,    .... 

375 

Parallax,    .         .         .90, 

389 

Right  ascension, 

23 

"         annual,    . 

387 

Right  sphere, 

83 

'*         horizontal,   . 

93 

"         how  found, 

94 

S. 

Parallel  sphere,  . 

84 

Sagittarius, 

370 

Parallels  of  latitude, 

24 

Saros,    .... 

192 

Pegasus,     .... 

373 

Saturn,       .... 

274 

Pendulum, 

79 

"        diameter  of, 

274 

Perigee,      .... 

187 

"        ring  of, 

275 

Periodical  inequalities,    . 

193 

"        satellites  of, 

282 

Perseus,      .   • 

371 

"        scenery  of, 

283 

Pisces,  .... 

371 

Scorpio, 

370 

Piscis  Australis, 

371 

Seasons,     .... 

119 

Planets, 

225 

Secondary, 

19 

distances  of,  . 

228 

Secular  inequalities,   . 

193 

inferior,     . 

227 

Serpent, 

373 

magnitudes  of, 

229 

Sextant,      .... 

57 

periods,     . 

229 

Sidereal  day, 

81 

superior, 

243 

"        month, 

173 

Pleiades, 

369 

Signs,     .... 

23 

Pointers,    .... 

374 

Sirius,         .... 

375 

Polar  distance, 

22 

Solstices, 

23 

Polaris,       .... 

373 

Sphere,  celestial, 

19 

Pole,      .... 

19 

"         doctrine  of  the,  . 

16 

"     of  the  earth, 

21 

"         oblique, 

84 

Pollux,  .... 

369 

"         parallel,     . 

84 

Power  of  the  Deity,  . 

408 

"         right,     . 

83 

Praesepe, 

369 

"        terrestrial, 

19 

Precession, 

155 

Spica,          .... 

370 

Prime  vertical, 

20 

Spots  on  the  sun,    . 

104 

Primum  mobile, 

398 

"                "    cause  of, 

106 

Principia, 

147 

"                "    dimensions  of, 

105 

Procyon,    .... 

375 

"                "   number  of,   . 

104 

Projection  of  the  sphere, 

27 

Stability  of  the  universe, 

410 

Proper  motions  of  the  stars, 

384 

Stars,  fixed, 

365 

Ptolemaic  system, 

399 

Stylus,    .... 

63 

Ptolemy, 

398 

Sun,  

101 

Pythagoras, 

394 

e     attraction  of  the,     . 

110 

*     density  of  the,     . 

103 

Q. 

*     diameter  of  the, 

102 

Quadrant, 

18 

c     distance  of  the,  . 

101 

*     mass  of  the,    . 

103 

R. 

*     nature   and  constitu- 

Radius,     .... 

17 

tion  of  the, 

107 

Refraction,     . 

95 

"     revolutions  of  the,  . 

104 

INDEX. 


419 


Sun,  spots  on  the, 

.    104 

U. 

'*     volume  of  the, 

,~      103 

Unity  of  the  Deity,     . 

.    407 

Supplement, 

.       18 

Uranus, 

283 

System  of  the  world, 

392-406 

diameter  of,    . 

.    283 

"        Brahean,    . 

403 

distance  of, 

284 

'*        Copernican,    . 

.    401 

history  of, 

.    284 

"        Ptolemaic, 

399 

period  of,    . 

284 

satellites  of,    . 

.    284 

T. 

scenery  of,        .*,- 

285 

Tangent,    . 

.    129 

Ursa  Major, 

.    373 

Taurus, 

369 

Ursa  Minor,  . 

373 

Telescope,  the,  . 

.      31 

achromatic, 

34 

V. 

directions  for  using,  39 

Variable  stars,    . 

.    379 

Dorpat, 

37 

Venus,  .... 

230 

Herschelian 

,       .      36 

conjunctions  of, 

.    231 

history  of 

33 

mountains  of, 

237 

reflecting, 

.      34 

phases  of, 

.    234 

Temperature,  changes 

of,        124 

revolutions  of, 

232 

Temporary  stars, 

.    380 

transits  of, 

.    239 

Terminator,  . 

119,  159 

Vesta,    .... 

288 

Thales,      . 

394 

Vindemiatrix, 

.    370 

Tides,    . 

.<•       216 

Virgo,    .         .         .  -   ,. 

370 

'      cause  of,  . 

.    216 

'      spring  and  neap, 

219 

Y. 

Time, 

.      59 

Year,  astronomical,    . 

.      63 

*      apparent, 

61 

"     tropical, 

156 

'      equation  of, 

.      61 

*      mean, 

61 

Z. 

*      sidereal,   .         . 

.      60 

Zenith, 

20 

Transits, 

237 

Zenith  distance, 

21 

Triangulation,    . 

.      75 

Zodiac, 

.      26 

Tropic, 

117 

Zodiacal  light, 

363 

Twilight,   . 

.      98    Zones, 

.      25 

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